How to find the area of a trapezoid

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

Questions 1 - 6

Trapezoid3

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

Explanation

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.

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

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

Screenshot_2015-03-29_at_3.18.30_pm

What is the area of the above trapezoid?

Explanation

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 .

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

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

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

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

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

Explanation

The find the area of a trapezoid, use:

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

Screenshot_2015-03-29_at_3.04.28_pm

What is the area of the above trapezoid?

Explanation

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:

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

Yard

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?

$20,500\textrm{ ft}^{2}$

$46,500 \textrm{ ft}^{2}$

$35,600 \textrm{ ft}^{2}$

$16,000 \textrm{ ft}^{2}$

$41,000 \textrm{ ft}^{2}$

Explanation

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.

Yard

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

$7,525 \textrm{ m}^{2}$

$8,925 \textrm{ m}^{2}$

$11,350 \textrm{ m}^{2}$

$6,125 \textrm{ m}^{2}$

$10,325 \textrm{ m}^{2}$

Explanation

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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