How to find the area of a trapezoid

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ACT Math › How to find the area of a trapezoid

Questions 1 - 5

Find the area of a trapezoid given bases of length 6 and 7 and height of 2.

$\frac{13}{2}$

Explanation

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

Substitute

into the area formula.

Thus,

$A=\frac{1}{2}(B1+B2)h=\frac{1}{2}(6+7)*2=6+7=13$

Trap

What is the area of the trapezoid above if a = 2, b = 6, and h = 4?

Explanation

Area of a Trapezoid = ½(a+b)*h

= ½ (2+6) * 4

= ½ (8) * 4

= 4 * 4 = 16

Find the area of a trapezoid if the height is , and the small and large bases are and , respectively.

Explanation

Write the formula to find the area of a trapezoid.

$A= \frac{1}{2} (b1+b2)h$

Substitute the givens and evaluate the area.

$A= \frac{1}{2} (b1+b2)h=\frac{1}{2} (2x+4x)(2x) = 2x^2+4x^2=6x^2$

Trapezoid has an area of . If height and , what is the measure of ?

Explanation

The formula for the area of a trapezoid is:

$A = \frac{b_1 + b_2}{2}* h$

We have here the height and one of the bases, plus the area, and we are being asked to find the length of base . Plug in known values and solve.

$525 = \frac{37 + b_2}{2}* 21$

$25 = \frac{37 + b_2}{2}$

Thus,

What is the area of this regular trapezoid?

Screen_shot_2013-03-18_at_3.27.27_pm

Explanation

To solve this question, you must divide the trapezoid into a rectangle and two right triangles. Using the Pythagorean Theorem, you would calculate the height of the triangle which is 4. The dimensions of the rectangle are 5 and 4, hence the area will be 20. The base of the triangle is 3 and the height of the triangle is 4. The area of one triangle is 6. Hence the total area will be 20+6+6=32. If you forget to split the shape into a rectangle and TWO triangles, or if you add the dimensions of the trapezoid, you could arrive at 26 as your answer.

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