Plane Geometry - ISEE Lower Level Quantitative Reasoning

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Question

What is the area of the parallelogram ABCD?

Answer

A parallelogram's area is found by multiplying its height by the base. The height of the parallelogram is not the side. It is the line that makes a right angle with the base. Therefore, the area of this parallelogram is:

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Question

What is the area of parallelogram ABCD?

Answer

A parallelogram's area is found by multiplying its height by the base. The height of the parallelogram is not the side. It is the line that makes a right angle with the base. Therefore, the area of this parallelogram is:

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Question

A parallelogram measures along its base and is high. Calculate the area.

Answer

The formula to calucate a parallelogram's area is:

$A = B \times H$

You calculate the parallelogram's area by multiplying its base by its height. Therefore, $A = 4 cm \times 7 cm$

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Question

A parallelogram measures along its base and is high. Calculate the area.

Answer

The formula to calucate a parallelogram's area is:

$A = B\times H$

You calculate the parallelogram's area by multiplying its base by its height. Therefore, $A = 6 cm \times 9 cm$

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Question

Find the area of a parallelogram whose height is and base is .

Answer

To solve, simply use the formula for the area of a parallelogram. Thus,

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Question

What is the area of a parallelogram if the base is , the other side is , and the height is ?

Answer

The area of a parallelogram is so the answer would be .

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Question

Find the area of the given parallelogram:

Answer

Find the area of the given parallelogram:

To find the area of a parallelogram, simply do the following:

Where b is the base, and h is the height. Note that the height is the length of the perpendicular line connecting both bases. In this case, our height is 12mi and our base is 144 miles.

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Question

Find the area of the given parallelogram:

Answer

Find the area of the given parallelogram:

To find the area of a parallelogram, simply use the following formula for area of a parallelogram:

Where b is the base, and h is the height. Note that the height is the length of the perpendicular line connecting both bases. In this case, our height is 12 mi and our base is 144 mi.

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Question

What is the perimeter of parallelogram ABCD?

Answer

The perimeter of a parallelogram is very easy to find. You just need to add up all the sides. However, you need to notice that the sides "across" from each other are equal on parallelograms. So, your figure could be redrawn:

The perimeter of your figure is therefore:

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Question

A parallelogram has a side length of . It also has a side length of . Calculate the perimeter.

Answer

A parallelogram has four sides and its opposite sides are equal in length. Therefore, if it has one side length of, it also has another side length of of . Since we know one of its side lenghts is , then the remaining side is . We can add all 4 side lengths $\left ( 3 in, 3 in, 5 in, 5in\right )$ to calculate the perimeter.

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Question

What is the perimeter of a parallelogram if the base is , the other side is , and the height is ?

Answer

The perimeter of a parallelogram is the sum of all four sides or the sum of two times each side length. The side lengths are and so the perimeter is .

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Question

Find the perimeter of the given parallelogram:

Answer

Find the perimeter of the given parallelogram:

The perimeter of any shape can be found by adding up the lentghs of its sides.

In this case, we have four sides. 2 that are 16 miles long, and 2 that are 144 miles long.

Find perimeter as follows:

Making our answer 320 miles

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Question

Find the area of the trapezoid.

Answer

Recall the formula for finding the area of a trapezoid:

$\text{Area}=\frac{base_1+base_2}{2}\times(height)$

Now, plug in the values for the bases and the height to find the area.

$\text{Area}=\frac{14+26}{2}\times(20)=400$

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Question

Find the area of the trapezoid.

Answer

Recall the formula for finding the area of a trapezoid:

$\text{Area}=\frac{base_1+base_2}{2}\times(height)$

Now, plug in the values for the bases and the height to find the area.

$\text{Area}=\frac{1+25}{2}\times(17)=221$

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Question

A trapezoid has two bases measuring and , and a height measuring

What is its area?

Answer

To find the area of a trapezoid, use this formula: $area= \frac{base +base}{2}\times height$ .

Use the information from the question to solve.

$a= \frac{3cm+5cm}{2}\times4cm$

$a=\frac{8cm}{2}\times 4cm$

$a=4cm\times 4cm=16cm^2$

The area is $16cm^{2}$ .

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Question

Calculate the area of the trapezoid:

Answer

Break the figure into a rectangle and a triangle. Use the dotted line as a guide. The rectangle has a length of 8 and a width of 6. The triangle has a base of 6 and width of 6.

Area of the rectangle:

$A=l\times w$

$A=6\times 8=48\ ft^2$

Area of the triangle:

$A=\frac{1}{2}b\times h$

$A=\frac{1}{2}\times 6\times 6=3\times 6=18\ ft^2$

Add them together:

$A=48\ ft^2+18\ ft^2=66\ ft^2$

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Question

Figure not drawn to scale

Find the area of the trapezoid.

Answer

In order to find the area of the trapezoid, we must follow the formula below:

$A=\frac{1}{2}(b_{1}+b_{2})h$

$b_{1}=$ One of the bases of the trapezoid

$b_{2}=$ The other base of the trapezoid

The height of the trapezoid

In this question, $b_{1}=10\ in$ , $b_{2}=14\ in$ , and $h=6\ in$

$A=\frac{1}{2}(b_{1}+b_{2})h\rightarrow A=\frac{1}{2}(10+14)6\rightarrow$

$A=\frac{1}{2}(24)6\rightarrow$

$A=126\rightarrow$

By following the formula and order of operations*, we are able to solve the problem. The area of the trapezoid is 72 in.2

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Question

Find the area of the trapezoid:

Answer

$A=\frac{1}{2}(b_1+b_2)(h)$

$A=\frac{1}{2}(6+10)(4)$

$A=\frac{1}{2}(16)(4)$

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Question

In a trapezoid, the top base is equal to 5 and the bottom base is equal to 11. It has a height of 6. What is the area?

Answer

The area of a trapezoid is equal to the sum of the bases, divided by 2, and then multiplied by the height:

$Area=\frac{base+base}{2}\cdot height$

$\frac{5+11}{2}\cdot 6$

$\frac{16}{2}\cdot 6$

$8\cdot 6$

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Question

A trapezoid's bases are and long. It's height is . What is the area of this trapezoid?

Answer

The formula to calculate the area of a trapezoid is:

$A = \frac{base + base}{2}\times height$

$A = \frac{6cm+8cm}{2cm}\times5cm$

$A= \frac{14cm}{2cm}\times5cm$

$A= 7cm\times5cm$

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