How to find the area of a trapezoid - ISEE Lower Level Quantitative Reasoning

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Question

What is the area of a trapezoid if its height is 1, its long base is 4, and its short base is 2?

Answer

The area of a trapezoid is given by the formula $\frac{1}{2} height (base_{long} + base_{short})$ .

We know that the height is 1, the long base is 4, and the short base is 2.

$\frac{1}{2} height (base_{long} + base_{short})=\frac{1}{2} (1) ((4) + (2))$

$\frac{1}{2}*(6)$

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Question

Which formula would you use to find the area of a trapezoid?

Answer

The find the area of a trapezoid, use:

$area=\left ( \frac{b1+b2}{2} \right )\times h$

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Question

Note: Figure NOT drawn to scale.

Mr. Smith owns the triangular piece of land seen in the above diagram. He sells the trapezoidal parcel shown at bottom right to his brother. What is the area of the land he retains?

Answer

The area of a triangle is half the product of its base and its height, so Mr. Smith's parcel originally had area

$\frac{1}{2 } \times 200 \times 250 = 25,000$ square feet.

The area of a trapezoid is the half product of its height and the sum of its two parallel sides (bases), so the portion Mr. Smith sold to his brother has area

$\frac{1}{2} \times 50 \times (80 + 100) = 4,500$ square feet.

Therefore, Mr. Smith retains a parcel of area

square feet.

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Question

The above diagram shows a trapezoidal home within a rectangular yard. What is the area of the yard?

Answer

The area of the yard is the area of the small trapezoid subtracted from that of the large rectangle. The area of a rectangle is the product of its length and its height, so the large rectangle has area

$105 \times 85 = 8,925$ square meters.

The area of a trapezoid is half the product of its height and the sum of its two parallel sides (bases), so the small trapezoid has area

$\frac{1}{2} \times 40 \times (30 + 40) = \frac{1}{2} \times 40 \times 70 = 1,400$ square meters.

The area of the yard is the difference of the two:

square meters.

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Question

What is the area of the above trapezoid?

Answer

The formula for the area of a trapezoid is $\frac{base_1 + base_2}{2}\cdot height$

In other words, find the average of the bases and multiply by the height. Substituting in the values of the bases for the given trapezoid, and , you get:

$\frac{9:in+7:in}{2}\cdot 5:in = 8:in\cdot 5:in=40:in^2$

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Question

What is the area of the above trapezoid?

Answer

The formula for the area of a trapezoid is $\frac{base_1 + base_2}{2}\cdot height$

In other words, find the average of the bases and multiply by the height. Substituting the values of the bases of the given trapezoid, and , into the equation, you get:

$\frac{8:cm+12:cm}{2}\cdot 5:cm = 10:cm\cdot 5:cm=50:cm^2$

The area of the trapezoid is thus .

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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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