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Pre-Algebra : Area

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Example Questions

Example Question #31 : Area Of A Triangle

Find the area of a triangle with a base of 4cm and a height that is two times the base.

Possible Answers:

$4\text{cm}^2$

$32\text{cm}$

$16\text{cm}$

$16\text{cm}^2$

$32\text{cm}^2$

Correct answer:

$16\text{cm}^2$

Explanation:

The formula to find the area of a triangle is

$A = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height. We know the base of our triangle is 4cm. We know the height is two times the base, so the height is 8cm. Now, we substitute

$A = \frac{1}{2} \cdot 4\text{cm} \cdot 8\text{cm}$

$A = 2\text{cm} \cdot 8\text{cm}$

$A = 16\text{cm}^2$

Therefore, the area of the triangle is $16\text{cm}^2$ .

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Example Question #33 : Area Of A Triangle

The base of a triangle is inches, and the height of the triangle is inches. What is the area of the triangle?

Possible Answers:

square inches

Correct answer:

square inches

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

square inches

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Example Question #34 : Area Of A Triangle

The base of a triangle is inches, and the height of the triangle is 8.9 inches. What is the area of the triangle?

Possible Answers:

55.4 square inches

51.4 square inches

53.3 square inches

52.4 square inches

53.4 square inches

Correct answer:

53.4 square inches

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

53.4 square inches

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Example Question #32 : Area Of A Triangle

The base of a triangle is inches, and the height of the triangle is inches. What is the area of the triangle?

Possible Answers:

$\frac{2xy}{2}$ square inches

$\frac{y}{2}$ square inches

$\frac{3x}{2}$ square inches

$\frac{x}{2}$ square inches

$\frac{xy}{2}$ square inches

Correct answer:

$\frac{xy}{2}$ square inches

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

$\frac{xy}{2}$ square inches

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Example Question #36 : Area Of A Triangle

The base of a triangle is inches, and the height of the triangle is inches. What is the area of the triangle?

Possible Answers:

square inches

14t square inches

square inches

Correct answer:

square inches

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

square inches

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Example Question #33 : Area Of A Triangle

A triangle with a base of 14 inches and height of 22 inches has an area of what?

Possible Answers:

36in^2

154in^2

84in^2

308in^2

77in^2

Correct answer:

154in^2

Explanation:

The formula for the area of a triangle is:

$\frac{1}{2} * base * height$

$\frac{1}{2} * 14 * 22 = 154in ^2$

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Example Question #34 : Area Of A Triangle

If Joan has a triangle-shaped plot for her garden, with the base measuring 3 ft and the heigh measuring 4 ft, what is the area of her garden?

Possible Answers:

ft^2

Correct answer:

ft^2

Explanation:

To find the area of a triangle, use the formula $\frac{1}{2}(b\times h)$ or $\frac{b\times h}{2}$

$\frac{1}{2}$ (3x4)=

$\frac{1}{2}(12)=$

square ft

$\frac{(3x4)}{2}=$

$\frac{12}{2}=$

square ft

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Example Question #1 : Area Of A Circle

A circle has a circumference of $\small 6\pi$ . What is its area?

Possible Answers:

$\small 9\pi$

$\small 6\pi$

$\small 12\pi$

$\small 18\pi$

$\small 36\pi$

Correct answer:

$\small 9\pi$

Explanation:

To begin, we need to find the radius of the circle. The circumference of a circle is given as follows:

$\small C = 2\pi r$ ,

where is the radius.

Then, a circle with circumference $6\pi$ will have the following radius:

$6\pi = 2\pi r$

$\small \frac{6\pi}{2\pi}=\frac{2\pi r}{2\pi}$

$\small 3=r$

Using the radius, we can now solve for the area:

$\small A=\pi r^2$

$A=\pi(3)^2$

$\small A=9\pi$

The area of the circle is $\small 9\pi$ .

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Example Question #2 : Area Of A Circle

What is the area of a circle with a diameter equal to ?

Possible Answers:

$12.25\pi$

$49\pi$

$24.5\pi$

$98\pi$

Correct answer:

$12.25\pi$

Explanation:

If the diameter is 7, then the radius is half of 7, or 3.5.

Plug this value for the radius into the equation for the area of a circle:

$A=r^2\pi=(3.5)^2\pi=12.25\pi$

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Example Question #2 : Area Of A Circle

Untitled_1

The rectangle in the above figure has length 20 and height 10. What is the area of the orange region?

Possible Answers:

$200 + 100 \pi$

$200 + 50 \pi$

$200 + \frac{25}{2} \pi$

$200 + 25 \pi$

Insufficient information is given to determine the area.

Correct answer:

$200 + \frac{25}{2} \pi$

Explanation:

The orange region is a composite of two figures:

One is a rectangle measuring 20 by 10, which, subsequently, has area

$20 \cdot 10 = 200$ .

The other is a semicircle with diameter 10, and, subsequently, radius 5. Its area is

$\frac{1}{2} \pi \cdot 5^{2} = \frac{25}{2} \pi$ .

Add the areas:

$A = 200 + \frac{25}{2} \pi$

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Pre-Algebra : Area

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #31 : Area Of A Triangle

Example Question #33 : Area Of A Triangle

Example Question #34 : Area Of A Triangle

Example Question #32 : Area Of A Triangle

Example Question #36 : Area Of A Triangle

Example Question #33 : Area Of A Triangle

Example Question #34 : Area Of A Triangle

Example Question #1 : Area Of A Circle

Example Question #2 : Area Of A Circle

Example Question #2 : Area Of A Circle

All Pre-Algebra Resources

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