Quadrilaterals - Math
Card 1 of 480
George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400 
and costs $40. One quart of paint covers 100 
and costs $15. How much money will he spend on the blue paint?
George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400
Tap to reveal answer
The area of the walls is given by 
One gallon of paint covers 400 
and the remaining 140 
would be covered by two quarts.
So one gallon and two quarts of paint would cost 
The area of the walls is given by
One gallon of paint covers 400
So one gallon and two quarts of paint would cost
← Didn't Know|Knew It →
If the area of rectangle is 52 meters squared and the perimeter of the same rectangle is 34 meters. What is the length of the larger side of the rectangle if the sides are integers?
If the area of rectangle is 52 meters squared and the perimeter of the same rectangle is 34 meters. What is the length of the larger side of the rectangle if the sides are integers?
Tap to reveal answer
Area of a rectangle is = lw
Perimeter = 2(l+w)
We are given 34 = 2(l+w) or 17 = (l+w)
possible combinations of l + w
are 1+16, 2+15, 3+14, 4+13... ect
We are also given the area of the rectangle is 52 meters squared.
Do any of the above combinations when multiplied together= 52 meters squared? yes 4x13 = 52
Therefore the longest side of the rectangle is 13 meters
Area of a rectangle is = lw
Perimeter = 2(l+w)
We are given 34 = 2(l+w) or 17 = (l+w)
possible combinations of l + w
are 1+16, 2+15, 3+14, 4+13... ect
We are also given the area of the rectangle is 52 meters squared.
Do any of the above combinations when multiplied together= 52 meters squared? yes 4x13 = 52
Therefore the longest side of the rectangle is 13 meters
← Didn't Know|Knew It →
Kayla took 25 minutes to walk around a rectangular city block. If the block's width is 1/4 the size of the length, how long would it take to walk along one length?
Kayla took 25 minutes to walk around a rectangular city block. If the block's width is 1/4 the size of the length, how long would it take to walk along one length?
Tap to reveal answer
Leaving the width to be x, the length is 4_x_. The total perimeter is 4_x_ + 4_x_ + x + x = 10x.
We divide 25 by 10 to get 2.5, the time required to walk the width. Therefore the time required to walk the length is (4)(2.5) = 10.
Leaving the width to be x, the length is 4_x_. The total perimeter is 4_x_ + 4_x_ + x + x = 10x.
We divide 25 by 10 to get 2.5, the time required to walk the width. Therefore the time required to walk the length is (4)(2.5) = 10.
← Didn't Know|Knew It →
A rectangle has a width of 2_x_. If the length is five more than 150% of the width, what is the perimeter of the rectangle?
A rectangle has a width of 2_x_. If the length is five more than 150% of the width, what is the perimeter of the rectangle?
Tap to reveal answer
Given that w = 2_x_ and l = 1.5_w_ + 5, a substitution will show that l = 1.5(2_x_) + 5 = 3_x_ + 5.
P = 2_w_ + 2_l_ = 2(2_x_) + 2(3_x_ + 5) = 4_x_ + 6_x_ + 10 = 10_x_ + 10 = 10(x + 1)
Given that w = 2_x_ and l = 1.5_w_ + 5, a substitution will show that l = 1.5(2_x_) + 5 = 3_x_ + 5.
P = 2_w_ + 2_l_ = 2(2_x_) + 2(3_x_ + 5) = 4_x_ + 6_x_ + 10 = 10_x_ + 10 = 10(x + 1)
← Didn't Know|Knew It →
Mark is making a plan to build a rectangular garden. He has 160 feet of fence to form the outside border of the garden. He wants the dimensions to look like the plan outlined below:
What is the area of the garden, rounded to the nearest square foot?
Mark is making a plan to build a rectangular garden. He has 160 feet of fence to form the outside border of the garden. He wants the dimensions to look like the plan outlined below:
What is the area of the garden, rounded to the nearest square foot?
Tap to reveal answer
Perimeter: Sum of the sides:
4x + 4x + 2x+8 +2x+8 = 160
12x + 6 = 160
12x = 154
x = 
Therefore, the short side of the rectangle is going to be:
And the long side is going to be:
The area of the rectangle is going to be as follows:
Area = lw
Perimeter: Sum of the sides:
4x + 4x + 2x+8 +2x+8 = 160
12x + 6 = 160
12x = 154
x =
Therefore, the short side of the rectangle is going to be:
And the long side is going to be:
The area of the rectangle is going to be as follows:
Area = lw
← Didn't Know|Knew It →
Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?
Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?
Tap to reveal answer
We know that the following represents the formula for the perimeter of a rectangle:
In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:
Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.
We also know that the length is two times the width; therefore, we can write the following:
The area of a rectangle is found by using this formula:
The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.
We know that the following represents the formula for the perimeter of a rectangle:
In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:
Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.
We also know that the length is two times the width; therefore, we can write the following:
The area of a rectangle is found by using this formula:
The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.
← Didn't Know|Knew It →
A contractor is going to re-tile a rectangular section of the kitchen floor. If the floor is 6ft x 3ft, and he is going to use square tiles with a side of 9in. How many tiles will be needed?
A contractor is going to re-tile a rectangular section of the kitchen floor. If the floor is 6ft x 3ft, and he is going to use square tiles with a side of 9in. How many tiles will be needed?
Tap to reveal answer
We have to be careful of our units. The floor is given in feet and the tile in inches. Since the floor is 6ft x 3ft. we can say it is 72in x 36in, because 12 inches equals 1 foot. If the tiles are 9in x 9in we can fit 8 tiles along the length and 4 tiles along the width. To find the total number of tiles we multiply 8 x 4 = 32. Alternately we could find the area of the floor (72 x 36, and divide by the area of the tile 9 x 9)
We have to be careful of our units. The floor is given in feet and the tile in inches. Since the floor is 6ft x 3ft. we can say it is 72in x 36in, because 12 inches equals 1 foot. If the tiles are 9in x 9in we can fit 8 tiles along the length and 4 tiles along the width. To find the total number of tiles we multiply 8 x 4 = 32. Alternately we could find the area of the floor (72 x 36, and divide by the area of the tile 9 x 9)
← Didn't Know|Knew It →
A rectangle has a perimeter of 40 inches. It is 3 times as long as it is wide. What is the area of the rectangle in square inches?
A rectangle has a perimeter of 40 inches. It is 3 times as long as it is wide. What is the area of the rectangle in square inches?
Tap to reveal answer
The width of the rectangle is w, therefore the length is 3w. The perimeter, P, can then be described as P = w + w + 3w +3w
40 = 8w
w = 5
width = 5, length = 3w = 15
A = 5*15 = 75 square inches
The width of the rectangle is w, therefore the length is 3w. The perimeter, P, can then be described as P = w + w + 3w +3w
40 = 8w
w = 5
width = 5, length = 3w = 15
A = 5*15 = 75 square inches
← Didn't Know|Knew It →
Angela is carpeting a rectangular conference room that measures 20 feet by 30 feet. If carpet comes in rectangular pieces that measures 5 feet by 4 feet, how many carpet pieces will she need to carpet the entire room?
Angela is carpeting a rectangular conference room that measures 20 feet by 30 feet. If carpet comes in rectangular pieces that measures 5 feet by 4 feet, how many carpet pieces will she need to carpet the entire room?
Tap to reveal answer
First, we need to find the area of the room. Because the room is rectangular, we can multiply 20 feet by 30 feet, which is 600 square feet. Next, we need to know how much space one carpet piece covers. Because the carpet pieces are also rectangular, we can multiply 4 feet by 5 feet to get 20 feet. To determine how many pieces of carpet Angela will need, we must divide the total square footage of the room (600 feet) by the square footage covered by one carpet piece (20 feet). 600 divided by 20 is 30, so Angela will need 30 carpet pieces to carpet the entire room.
First, we need to find the area of the room. Because the room is rectangular, we can multiply 20 feet by 30 feet, which is 600 square feet. Next, we need to know how much space one carpet piece covers. Because the carpet pieces are also rectangular, we can multiply 4 feet by 5 feet to get 20 feet. To determine how many pieces of carpet Angela will need, we must divide the total square footage of the room (600 feet) by the square footage covered by one carpet piece (20 feet). 600 divided by 20 is 30, so Angela will need 30 carpet pieces to carpet the entire room.
← Didn't Know|Knew It →
Find the perimeter of the following kite:
Find the perimeter of the following kite:
Tap to reveal answer
The formula for the perimeter of a kite is:
Where 
is the length of the longer side and 
is the length of the shorter side
Use the formulas for a 
triangle and a 
triangle to find the lengths of the longer sides. The formula for a 
triangle is 
and the formula for a 
triangle is 
.
Our 
triangle is: 
Our 
triangle is: 
Plugging in our values, we get:
The formula for the perimeter of a kite is:
Where
Use the formulas for a
Our
Our
Plugging in our values, we get:
← Didn't Know|Knew It →
What is the area of a kite with diagonals of 5 and 7?
What is the area of a kite with diagonals of 5 and 7?
Tap to reveal answer
To find the area of a kite using diagonals you use the following equation 
That diagonals (
and 
)are the lines created by connecting the two sides opposite of each other.
Plug in the diagonals for 
and 
to get 
Then multiply and divide to get the area. 
The answer is 
To find the area of a kite using diagonals you use the following equation
That diagonals (
Plug in the diagonals for
Then multiply and divide to get the area.
The answer is
← Didn't Know|Knew It →
Find the area of the following kite:
Find the area of the following kite:
Tap to reveal answer
The formula for the area of a kite is:
Where 
is the length of one diagonal and 
is the length of the other diagonal
Plugging in our values, we get:
The formula for the area of a kite is:
Where
Plugging in our values, we get:
← Didn't Know|Knew It →
Find the area of the following kite:
Find the area of the following kite:
Tap to reveal answer
The formula for the area of a kite is:
where 
is the length of one diagonal and 
is the length of another diagonal.
Use the formulas for a triangle and a triangle to find the lengths of the diagonals. The formula for a triangle is and the formula for a triangle is 
.
Our triangle is:
Our triangle is: 
Plugging in our values, we get:
The formula for the area of a kite is:
where
Use the formulas for a
Our
Our
Plugging in our values, we get:
← Didn't Know|Knew It →
Find the perimeter of the following kite:
Find the perimeter of the following kite:
Tap to reveal answer
In order to find the length of the two shorter edges, use a Pythagorean triple:
In order to find the length of the two longer edges, use the Pythagorean theorem:
The formula of the perimeter of a kite is:
Plugging in our values, we get:
In order to find the length of the two shorter edges, use a Pythagorean triple:
In order to find the length of the two longer edges, use the Pythagorean theorem:
The formula of the perimeter of a kite is:
Plugging in our values, we get:
← Didn't Know|Knew It →
If the width of a rectangle is 8 inches, and the length is half the width, what is the area of the rectangle in square inches?
If the width of a rectangle is 8 inches, and the length is half the width, what is the area of the rectangle in square inches?
Tap to reveal answer
the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.
The area of the rectangle can be determined from multiplying length by width, so,
4 x 8 = 32 inches squared
the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.
The area of the rectangle can be determined from multiplying length by width, so,
4 x 8 = 32 inches squared
← Didn't Know|Knew It →
Find the measure of angle 
in the isosceles trapezoid pictured below.
Find the measure of angle
Tap to reveal answer
The sum of the angles in any quadrilateral is 360**°, and the properties of an isosceles trapezoid dictate that the sets of angles adjoined by parallel lines (in this case, the bottom set and top set of angles) are equal. Subtracting 2(72°) from 360°** gives the sum of the two top angles, and dividing the resulting 216**°** by 2 yields the measurement of x, which is 108**°**.
The sum of the angles in any quadrilateral is 360**°, and the properties of an isosceles trapezoid dictate that the sets of angles adjoined by parallel lines (in this case, the bottom set and top set of angles) are equal. Subtracting 2(72°) from 360°** gives the sum of the two top angles, and dividing the resulting 216**°** by 2 yields the measurement of x, which is 108**°**.
← Didn't Know|Knew It →
What is the area of this regular trapezoid?
What is the area of this regular trapezoid?
Tap to reveal answer
To solve this question, you must divide the trapezoid into a rectangle and two right triangles. Using the Pythagorean Theorem, you would calculate the height of the triangle which is 4. The dimensions of the rectangle are 5 and 4, hence the area will be 20. The base of the triangle is 3 and the height of the triangle is 4. The area of one triangle is 6. Hence the total area will be 20+6+6=32. If you forget to split the shape into a rectangle and TWO triangles, or if you add the dimensions of the trapezoid, you could arrive at 26 as your answer.
To solve this question, you must divide the trapezoid into a rectangle and two right triangles. Using the Pythagorean Theorem, you would calculate the height of the triangle which is 4. The dimensions of the rectangle are 5 and 4, hence the area will be 20. The base of the triangle is 3 and the height of the triangle is 4. The area of one triangle is 6. Hence the total area will be 20+6+6=32. If you forget to split the shape into a rectangle and TWO triangles, or if you add the dimensions of the trapezoid, you could arrive at 26 as your answer.
← Didn't Know|Knew It →
What is the area of the trapezoid above if a = 2, b = 6, and h = 4?
What is the area of the trapezoid above if a = 2, b = 6, and h = 4?
Tap to reveal answer
Area of a Trapezoid = ½(a+b)*h
= ½ (2+6) * 4
= ½ (8) * 4
= 4 * 4 = 16
Area of a Trapezoid = ½(a+b)*h
= ½ (2+6) * 4
= ½ (8) * 4
= 4 * 4 = 16
← Didn't Know|Knew It →
A trapezoid has a base of length 4, another base of length s, and a height of length s. A square has sides of length s. What is the value of s such that the area of the trapezoid and the area of the square are equal?
A trapezoid has a base of length 4, another base of length s, and a height of length s. A square has sides of length s. What is the value of s such that the area of the trapezoid and the area of the square are equal?
Tap to reveal answer
In general, the formula for the area of a trapezoid is (1/2)(a + b)(h), where a and b are the lengths of the bases, and h is the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:
area of trapezoid = (1/2)(4 + s)(s)
Similarly, the area of a square with sides of length a is given by _a_2. Thus, the area of the square given in the problem is _s_2.
We now can set the area of the trapezoid equal to the area of the square and solve for s.
(1/2)(4 + s)(s) = _s_2
Multiply both sides by 2 to eliminate the 1/2.
(4 + s)(s) = 2_s_2
Distribute the s on the left.
4_s_ + _s_2 = 2_s_2
Subtract _s_2 from both sides.
4_s_ = _s_2
Because s must be a positive number, we can divide both sides by s.
4 = s
This means the value of s must be 4.
The answer is 4.
In general, the formula for the area of a trapezoid is (1/2)(a + b)(h), where a and b are the lengths of the bases, and h is the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:
area of trapezoid = (1/2)(4 + s)(s)
Similarly, the area of a square with sides of length a is given by _a_2. Thus, the area of the square given in the problem is _s_2.
We now can set the area of the trapezoid equal to the area of the square and solve for s.
(1/2)(4 + s)(s) = _s_2
Multiply both sides by 2 to eliminate the 1/2.
(4 + s)(s) = 2_s_2
Distribute the s on the left.
4_s_ + _s_2 = 2_s_2
Subtract _s_2 from both sides.
4_s_ = _s_2
Because s must be a positive number, we can divide both sides by s.
4 = s
This means the value of s must be 4.
The answer is 4.
← Didn't Know|Knew It →
This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in.
What is the area of the isoceles trapezoid?
This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in.
What is the area of the isoceles trapezoid?
Tap to reveal answer
In order to find the area of an isoceles trapezoid, you must average the bases and multiply by the height.
The average of the bases is straight forward:
In order to find the height, you must draw an altitude. This creates a right triangle in which one of the legs is also the height of the trapezoid. You may recognize the Pythagorean triple (6-8-10) and easily identify the height as 8. Otherwise, use 
.
Multiply the average of the bases (12) by the height (8) to get an area of 96.
In order to find the area of an isoceles trapezoid, you must average the bases and multiply by the height.
The average of the bases is straight forward:
In order to find the height, you must draw an altitude. This creates a right triangle in which one of the legs is also the height of the trapezoid. You may recognize the Pythagorean triple (6-8-10) and easily identify the height as 8. Otherwise, use
Multiply the average of the bases (12) by the height (8) to get an area of 96.
← Didn't Know|Knew It →