How to find the perimeter of a figure - HSPT Math
Card 1 of 524
Note: Figure NOT drawn to scale.
, where 
and 
represent side lengths of the parallelogram and 
represents the height.
Find the perimeter of the parallelogram in the diagram.
Note: Figure NOT drawn to scale.
Find the perimeter of the parallelogram in the diagram.
Tap to reveal answer
The perimeter of the parallelogram is the sum of the four side lengths - here, that formula becomes
.
Note that the height 
is irrelevant to the answer.
The perimeter of the parallelogram is the sum of the four side lengths - here, that formula becomes
Note that the height
← Didn't Know|Knew It →
What is the perimeter of a figure with seven sides, four of which measure 9 inches, two of which measure 10 inches, and one of which measures a foot?
What is the perimeter of a figure with seven sides, four of which measure 9 inches, two of which measure 10 inches, and one of which measures a foot?
Tap to reveal answer
Add the side measures, in inches (changing one foot to 12 inches):
Add the side measures, in inches (changing one foot to 12 inches):
← Didn't Know|Knew It →
How many meters of fence are needed to enclose a rectangular field that has a length of 1000 meters and a width of 100 meters?
How many meters of fence are needed to enclose a rectangular field that has a length of 1000 meters and a width of 100 meters?
Tap to reveal answer
The perimeter of a rectangle is simply the sum of the four sides:
The perimeter of a rectangle is simply the sum of the four sides:
← Didn't Know|Knew It →
ABCD is a parallelogram. BD = 5. The angles of triangle ABD are all equal. What is the perimeter of the parallelogram?
ABCD is a parallelogram. BD = 5. The angles of triangle ABD are all equal. What is the perimeter of the parallelogram?
Tap to reveal answer
If all of the angles in triangle ABD are equal and line BD divides the parallelogram, then all angles in triangle BDC must be equal as well.
We now have two equilateral triangles, so all sides of the triangles will be equal.
All sides therefore equal 5.
5+5+5+5 = 20
If all of the angles in triangle ABD are equal and line BD divides the parallelogram, then all angles in triangle BDC must be equal as well.
We now have two equilateral triangles, so all sides of the triangles will be equal.
All sides therefore equal 5.
5+5+5+5 = 20
← Didn't Know|Knew It →
A circle with a radius 2 in is inscribed in a square. What is the perimeter of the square?
A circle with a radius 2 in is inscribed in a square. What is the perimeter of the square?
Tap to reveal answer
To inscribe means to draw inside a figure so as to touch in as many places as possible without overlapping. The circle is inside the square such that the diameter of the circle is the same as the side of the square, so the side is actually 4 in. The perimeter of the square = 4s = 4 * 4 = 16 in.
To inscribe means to draw inside a figure so as to touch in as many places as possible without overlapping. The circle is inside the square such that the diameter of the circle is the same as the side of the square, so the side is actually 4 in. The perimeter of the square = 4s = 4 * 4 = 16 in.
← Didn't Know|Knew It →
Square X has 3 times the area of Square Y. If the perimeter of Square Y is 24 ft, what is the area of Square X, in sq ft?
Square X has 3 times the area of Square Y. If the perimeter of Square Y is 24 ft, what is the area of Square X, in sq ft?
Tap to reveal answer
Find the area of Square Y, then calculate the area of Square X.
If the perimeter of Square Y is 24, then each side is 24/4, or 6.
A = 6 * 6 = 36 sq ft, for Square Y
If Square X has 3 times the area, then 3 * 36 = 108 sq ft.
Find the area of Square Y, then calculate the area of Square X.
If the perimeter of Square Y is 24, then each side is 24/4, or 6.
A = 6 * 6 = 36 sq ft, for Square Y
If Square X has 3 times the area, then 3 * 36 = 108 sq ft.
← Didn't Know|Knew It →
A square rug border consists of a continuous pattern of equilateral triangles, with isosceles triangles as corners, one of which is shown above. If the length of each equilateral triangle side is 5 inches, and there are 40 triangles in total, what is the total perimeter of the rug?
The inner angles of the corner triangles is 30°.
A square rug border consists of a continuous pattern of equilateral triangles, with isosceles triangles as corners, one of which is shown above. If the length of each equilateral triangle side is 5 inches, and there are 40 triangles in total, what is the total perimeter of the rug?
The inner angles of the corner triangles is 30°.
Tap to reveal answer
There are 2 components to this problem. The first, and easier one, is recognizing how much of the perimeter the equilateral triangles take up—since there are 40 triangles in total, there must be 40 – 4 = 36 of these triangles. By observation, each contributes only 1 side to the overall perimeter, thus we can simply multiply 36(5) = 180" contribution.
The second component is the corner triangles—recognizing that the congruent sides are adjacent to the 5-inch equilateral triangles, and the congruent angles can be found by
180 = 30+2x → x = 75°
We can use ratios to find the unknown side:
75/5 = 30/y → 75y = 150 → y = 2''.
Since there are 4 corners to the square rug, 2(4) = 8'' contribution to the total perimeter. Adding the 2 components, we get 180+8 = 188 inch perimeter.
There are 2 components to this problem. The first, and easier one, is recognizing how much of the perimeter the equilateral triangles take up—since there are 40 triangles in total, there must be 40 – 4 = 36 of these triangles. By observation, each contributes only 1 side to the overall perimeter, thus we can simply multiply 36(5) = 180" contribution.
The second component is the corner triangles—recognizing that the congruent sides are adjacent to the 5-inch equilateral triangles, and the congruent angles can be found by
180 = 30+2x → x = 75°
We can use ratios to find the unknown side:
75/5 = 30/y → 75y = 150 → y = 2''.
Since there are 4 corners to the square rug, 2(4) = 8'' contribution to the total perimeter. Adding the 2 components, we get 180+8 = 188 inch perimeter.
← Didn't Know|Knew It →
Two sides of an isosceles triangle are 20 and 30. What is the difference of the largest and the smallest possible perimeters?
Two sides of an isosceles triangle are 20 and 30. What is the difference of the largest and the smallest possible perimeters?
Tap to reveal answer
The trick here is that we don't know which is the repeated side. Our possible triangles are therefore 20 + 20 + 30 = 70 or 30 + 30 + 20 = 80. The difference is therefore 80 – 70 or 10.
The trick here is that we don't know which is the repeated side. Our possible triangles are therefore 20 + 20 + 30 = 70 or 30 + 30 + 20 = 80. The difference is therefore 80 – 70 or 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 →
A square has an area of 
. If the side of the square is reduced by a factor of two, what is the perimeter of the new square?
A square has an area of
Tap to reveal answer
The area of the given square is given by 
so the side must be 6 in. The side is reduced by a factor of two, so the new side is 3 in. The perimeter of the new square is given by 
.
The area of the given square is given by
← Didn't Know|Knew It →
What is the perimeter of a rectangle with a width of 3 and a length of 10?
What is the perimeter of a rectangle with a width of 3 and a length of 10?
Tap to reveal answer
The formula for the perimeter of a rectangle is 
.
Plug in our given values to solve:
The formula for the perimeter of a rectangle is
Plug in our given values to solve:
← Didn't Know|Knew It →
What is the perimeter of a right triangle with hypotenuse 
and a leg of length 
?
What is the perimeter of a right triangle with hypotenuse
Tap to reveal answer
Using the Pythagorean Theorem, the length of the second leg can be determined.
We are given the length of the hypotenuse and one leg.
The perimeter of the triangle is the sum of the lengths of the sides.
Using the Pythagorean Theorem, the length of the second leg can be determined.
We are given the length of the hypotenuse and one leg.
The perimeter of the triangle is the sum of the lengths of the sides.
← Didn't Know|Knew It →
Sandy wants to put a border around her son’s nursery. If all four square walls in the room have the same width and use up 
feet of border, what is the length of one wall?
Sandy wants to put a border around her son’s nursery. If all four square walls in the room have the same width and use up
Tap to reveal answer
When Sandy puts the border around her son's room, she will need enough to cover the perimeter. Since the room has four walls equal in length, we know that the room is a square. The perimeter of a square can by found by adding all the sides together, or by multiplying the length of one side by 4. This can be written as:
Since we know that Sandy used 
feet of border, we know the perimeter is 
. We can now write an equation:
Now, in order to isolate the variable, we can divide both sides by four.
The left-hand side simplifies to:
The right-hand side simplifies to:
When we solve, we find that the length of each wall is 
.
When Sandy puts the border around her son's room, she will need enough to cover the perimeter. Since the room has four walls equal in length, we know that the room is a square. The perimeter of a square can by found by adding all the sides together, or by multiplying the length of one side by 4. This can be written as:
Since we know that Sandy used
Now, in order to isolate the variable, we can divide both sides by four.
The left-hand side simplifies to:
The right-hand side simplifies to:
When we solve, we find that the length of each wall is
← Didn't Know|Knew It →
Find the perimeter of the parallelogram.
Find the perimeter of the parallelogram.
Tap to reveal answer
To find the perimeter of a parallelogram, add the lengths of the sides. Opposite sides of a parallelogram are equivalent.
To find the perimeter of a parallelogram, add the lengths of the sides. Opposite sides of a parallelogram are equivalent.
← Didn't Know|Knew It →
The perimeter of the following trapezoid is equal to 23 cm. Solve for 
. (Figure not drawn to scale.)
The perimeter of the following trapezoid is equal to 23 cm. Solve for
Tap to reveal answer
The perimeter is equal to the sum of all of the sides.
The perimeter is equal to the sum of all of the sides.
← Didn't Know|Knew It →
Give the perimeter of the above rectangle in centimeters, using the conversion factor 
centimeters per yard.
Give the perimeter of the above rectangle in centimeters, using the conversion factor
Tap to reveal answer
The perimeter of the rectangle is 
yards. To convert this to centimeters, multiply by the given conversion factor:
centimeters.
The perimeter of the rectangle is
← Didn't Know|Knew It →
Find the perimenter:
Find the perimenter:
Tap to reveal answer
The perimeter is equal to the sum of the length of all sides. Each side is equal to 
. Therefore, the perimeter equals:
The perimeter is equal to the sum of the length of all sides. Each side is equal to
← Didn't Know|Knew It →
Use this image for the following problem.
What is the perimeter of the square in this picture?
Use this image for the following problem.
What is the perimeter of the square in this picture?
Tap to reveal answer
The question only is looking for a part of the picture, just the square. With squares, the rule is that all the sides are equivalent, meaning the same lengths and all angles are right angles.
Perimeter means adding up all the sides together. So we just need to add the lengths of the sides of the square. Uh oh, we only have one side that is listed.
Again, remember that with squares the sides are equivalent, and we know one side is 5 inches. We just need to take 
because a square has 4 sides.
Our perimeter is 
.
The question only is looking for a part of the picture, just the square. With squares, the rule is that all the sides are equivalent, meaning the same lengths and all angles are right angles.
Perimeter means adding up all the sides together. So we just need to add the lengths of the sides of the square. Uh oh, we only have one side that is listed.
Again, remember that with squares the sides are equivalent, and we know one side is 5 inches. We just need to take
Our perimeter is
← Didn't Know|Knew It →
You are given equilateral triangle 
and Rectangle 
with 
.
What is the perimeter of Rectangle 
?
You are given equilateral triangle
with
What is the perimeter of Rectangle
Tap to reveal answer
is equilateral, so 
.
Also, since opposite sides of a rectangle are congruent,
and 
The perimeter of Rectangle 
is
Also, since opposite sides of a rectangle are congruent,
The perimeter of Rectangle
← Didn't Know|Knew It →
The length of a rectangle is two times as long as the width. The width is equal to 
inches. What is the perimeter of the rectangle?
The length of a rectangle is two times as long as the width. The width is equal to
Tap to reveal answer
← Didn't Know|Knew It →