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High School Math : How to find the area of a trapezoid

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Example Questions

Example Question #7 : Quadrilaterals

Find the area of the following trapezoid:

Trapezoid

Possible Answers:

260m^2

202m^2

180m^2

252m^2

126m^2

Correct answer:

252m^2

Explanation:

The formula for the area of a trapezoid is:

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

Where b_1 is the length of one base, b_2 is the length of the other base, and is the height.

To find the height of the trapezoid, use a Pythagorean triple:

5-12-13

5m-12m-13m

Plugging in our values, we get:

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

$A = \frac{1}{2}(16m+26m)(12m)=252m^2$

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Example Question #8 : Quadrilaterals

Find the area of the following trapezoid:

Trapezoid_angles

Possible Answers:

$96+24\sqrt{3}m^2$

$48+24\sqrt{3}m^2$

$60+24\sqrt{3}m^2$

$54+24\sqrt{6}m^2$

$96+12\sqrt{3}m^2$

Correct answer:

$96+24\sqrt{3}m^2$

Explanation:

Use the formula for 30-60-90 triangles in order to find the length of the bottom base and the height.

The formula is:

$a-a\sqrt{3}-2a$

Where is the length of the side opposite the $\measuredangle 30$ .

Beginning with the 12m side, if we were to create a 30-60-90 triangle, the length of the base is $6\sqrt{3}m$ , and the height is .

Creating another 30-60-90 triangle on the left, we find the height is , the length of the base is $2\sqrt{3}m$ , and the side is $4\sqrt{3}m$ .

The formula for the area of a trapezoid is:

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

Where b_1 is the length of one base, b_2 is the length of the other base, and is the height.

Plugging in our values, we get:

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

$A = \frac{1}{2}(16m+16m+6\sqrt{3}m+2\sqrt{3}m)(6m)$

$A = \frac{1}{2}(32m+8\sqrt{3}m)(6m)$

$A = (32m+8\sqrt{3}m)(3m)=96+24\sqrt{3}m^2$

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Example Question #9 : Quadrilaterals

Determine the area of the following trapezoid:

Screen_shot_2014-02-27_at_6.39.24_pm

Possible Answers:

25m^2

24m^2

28m^2

20m^2

35m^2

Correct answer:

24m^2

Explanation:

The formula for the area of a trapezoid is:

$A=\frac{1}{2}(b_{1}+b_{2})(h)$ ,

where b_1 is the length of one base, b_2 is the length of another base, and is the length of the height.

Plugging in our values, we get:

$A=\frac{1}{2}(7m+5m)(4m)=24m^2$

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Example Question #10 : Quadrilaterals

Find the area of the following trapezoid:

Screen_shot_2014-02-27_at_6.47.22_pm

Possible Answers:

$52\sqrt{101}m^2$

$48\sqrt{81}m^2$

$48\sqrt{101}m^2$

$48\sqrt{91}m^2$

$52\sqrt{91}m^2$

Correct answer:

$48\sqrt{91}m^2$

Explanation:

The formula for the area of a trapezoid is:

$A=\frac{1}{2}(b_{1}+b_{2})(h)$ ,

where b_1 is the length of one base, b_2 is the length of another base, and is the length of the height.

Use the Pythagorean Theorem to find the height of the trapezoid:

A^2+B^2=C^2

6m^2+B^2=20m^2

$B=2\sqrt{91}m$

Plugging in our values, we get:

$A=\frac{1}{2}(18m+30m)(2\sqrt{91}m)=48\sqrt{91}m^2$

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Example Question #1 : How To Find The Area Of A Trapezoid

Find the area of the following trapezoid:

Possible Answers:

$146\ m^2$

$138\ m^2$

$144\ m^2$

$142\ m^2$

$140\ m^2$

Correct answer:

$144\ m^2$

Explanation:

The formula for the area of a trapezoid is

A = (median)(height) .

Use the Pythagorean Theorem to find the length of the height:

A^2 + B^2 = C^2

$(5\ m)^2 + B^2 = (13\ m)^2$

$B = 12\ m$

Plugging in our values, we get:

$A = (12\ m)(12\ m)$

$A = 144\ m^2$

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Example Question #1 : How To Find The Area Of A Trapezoid

Find the area of the following trapezoid:

Possible Answers:

$\frac{125+125\sqrt{3}\ m^2}{2}$

$\frac{125+25\sqrt{3}\ m^2}{2}$

$\frac{125+25\sqrt{2}\ m^2}{3}$

$\frac{25+125\sqrt{3}\ m^2}{2}$

$\frac{25+25\sqrt{3}\ m^2}{2}$

Correct answer:

$\frac{125+25\sqrt{3}\ m^2}{2}$

Explanation:

The formula for the area of a trapezoid is

$A = \frac{1}{2}(b_1+b_2)(h)$ ,

where is the base of the trapezoid and is the height of the trapezoid.

Use the formula for a 30-60-90 triangle to find the length of the base and height:

$a-2a-a\sqrt{3}$

$5\ m-10\ m-5\sqrt{3}\ m$

Use the formula for a 45-45-90 triangle to find the length of the base and height:

a-a-2a

$5\ m-5\ m-5\sqrt{2}\ m$

Plugging in our values, we get:

$A = \frac{1}{2}(10\ m+5\ m+10\ m+5\sqrt{3}\ m)(5\ m)$

$A = \frac{125+25\sqrt{3}\ m^2}{2}$

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Example Question #1 : How To Find The Area Of A Trapezoid

What is the area of this regular trapezoid?

Screen_shot_2013-03-18_at_3.27.27_pm

Possible Answers:

Correct answer:

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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Example Question #1 : How To Find The Area Of A Trapezoid

Trap

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

Possible Answers:

Correct answer:

Explanation:

Area of a Trapezoid = ½(a+b)*h

= ½ (2+6) * 4

= ½ (8) * 4

= 4 * 4 = 16

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Example Question #1 : Trapezoids

A trapezoid has a base of length 4, another base of length s, and a height of length s. A square has sides of length s. What is the value of s such that the area of the trapezoid and the area of the square are equal?

Possible Answers:

$\sqrt{2}$

$2\sqrt{2}$

Correct answer:

Explanation:

In general, the formula for the area of a trapezoid is (1/2)(a + b)(h), where a and b are the lengths of the bases, and h is the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:

area of trapezoid = (1/2)(4 + s)(s)

Similarly, the area of a square with sides of length a is given by a². Thus, the area of the square given in the problem is s².

We now can set the area of the trapezoid equal to the area of the square and solve for s.

(1/2)(4 + s)(s) = s²

Multiply both sides by 2 to eliminate the 1/2.

(4 + s)(s) = 2s²

Distribute the s on the left.

4s + s² = 2s²

Subtract s² from both sides.

4s = s²

Because s must be a positive number, we can divide both sides by s.

4 = s

This means the value of s must be 4.

The answer is 4.

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Example Question #6 : How To Find The Area Of A Trapezoid

This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in. Isoceles_trapezoid

What is the area of the isoceles trapezoid?

Possible Answers:

180

120

Correct answer:

Explanation:

In order to find the area of an isoceles trapezoid, you must average the bases and multiply by the height.

The average of the bases is straight forward:

$\frac{6+18}{2}=12$

In order to find the height, you must draw an altitude. This creates a right triangle in which one of the legs is also the height of the trapezoid. You may recognize the Pythagorean triple (6-8-10) and easily identify the height as 8. Otherwise, use $a^{2}+b^{2}=c^{2}$ .

$36+b^{2}=100$

$b^{2}=64$

b=8

Multiply the average of the bases (12) by the height (8) to get an area of 96.

Isoceles_trapezoid_explained

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High School Math : How to find the area of a trapezoid

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #7 : Quadrilaterals

Example Question #8 : Quadrilaterals

Example Question #9 : Quadrilaterals

Example Question #10 : Quadrilaterals

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #1 : Trapezoids

Example Question #6 : How To Find The Area Of A Trapezoid

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