Geometry - ISEE Lower Level Quantitative Reasoning

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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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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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