Quadrilaterals - ISEE Lower Level Quantitative Reasoning

Card 0 of 1825

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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Question

Find the area of a trapezoid whose bases are and and height is .

Answer

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

$A=\frac{1}{2}(B1+B2)h=\frac{1}{2}(4+6)5=\frac{1}{2}10*5=25$

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Question

Find the area of a trapezoid with bases and , and height .

Answer

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

$A=\frac{1}{2}(b1+b2)h=\frac{1}{2}(5+4)6=\frac{1}{2}9*6=27$

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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.

$\text{Area}=\frac{9+30}{2}\times(15)=292.5$

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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.

$\text{Area}=\frac{15+30}{2}\times(25)=562.5$

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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.

$\text{Area}=\frac{2+20}{2}\times(9)=99$

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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.

$\text{Area}=\frac{6+20}{2}\times(16)=208$

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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.

$\text{Area}=\frac{9+3}{2}\times(5)=30$

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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.

$\text{Area}=\frac{3+6}{2}\times(4)=18$

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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.

$\text{Area}=\frac{11+5}{2}\times(6)=48$

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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.

$\text{Area}=\frac{2+4}{2}\times(4)=12$

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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.

$\text{Area}=\frac{3+1}{2}\times(4)=8$

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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.

$\text{Area}=\frac{3+25}{2}\times(12)=168$

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Question

Figure not drawn to scale

Find the perimeter of the trapezoid.

Answer

In order to find the perimeter of the trapezoid, you must add up the lengths of all the sides of the trapezoid.

Because the lengths of the trapezoid are in inches, the answer is 40 in.

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