Area

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Pre-Algebra › Area

Questions 1 - 10

1

What is the area of the triangle?

Question_11

$\small 35$

$\small 70$

$\small 84$

$\small 42$

Explanation

Area of a triangle can be determined using the equation:

$\small A=\frac{1}{2}bh$

$\small A=\frac{1}{2}(14)(5)=35$

2

What is the area of the triangle?

Question_11

$\small 35$

$\small 70$

$\small 84$

$\small 42$

Explanation

Area of a triangle can be determined using the equation:

$\small A=\frac{1}{2}bh$

$\small A=\frac{1}{2}(14)(5)=35$

3

If a circular island has a diameter of 12 miles, what is the area of the island?

$36\pi$

$16\pi$

$2\pi$

$12\pi$

Explanation

The formula for the area of a circle is $\pi r ^{2}$ ("" is for radius). However, the question only gives us the diameter, so we must determine the radius ourselves first.

A radius is half a diameter, therefore if the diameter is 12 miles then the radius is 6 miles.

Now we can plug in 6 for "" and solve.
$\pi (6^{2}) =$
$36\pi$

4

If a circular island has a diameter of 12 miles, what is the area of the island?

$36\pi$

$16\pi$

$2\pi$

$12\pi$

Explanation

The formula for the area of a circle is $\pi r ^{2}$ ("" is for radius). However, the question only gives us the diameter, so we must determine the radius ourselves first.

A radius is half a diameter, therefore if the diameter is 12 miles then the radius is 6 miles.

Now we can plug in 6 for "" and solve.
$\pi (6^{2}) =$
$36\pi$

5

What is the area of a circle with a diameter equal to 6?

$9\pi$

$3\pi$

$18\pi$

$36\pi$

Explanation

First, solve for radius:

$r=\frac{d}{2}=\frac{6}{2}=3$

Then, solve for area:

$A=r^2\pi=3^2\pi=9\pi$

6

What is the area of a circle with a diameter of , rounded to the nearest whole number?

$\dpi{100} 64$

$\dpi{100} 254$

$\dpi{100} 255$

$\dpi{100} 81$

Explanation

The formula for the area of a circle is

$\dpi{100} \pi r^{2}$

Find the radius by dividing 9 by 2:

$\dpi{100} \frac{9}{2}=4.5$

So the formula for area would now be:

$\dpi{100} \pi r^{2}=\pi (4.5)^{2}=20.25\pi \approx 63.6= 64$

7

The diameter of a circle is . Give the area of the circle in terms of .

Explanation

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle and $\pi$ is approximately .

$Area=\frac{\pi (4t)^2}{4}=\frac{16\pi t^2}{4}=4\pi t^2 \Rightarrow Area\approx 4\times 3.14\times t^2$

$\Rightarrow Area\approx 12.56t^2$

8

Solve for the area of a circle if the radius is .

$4\pi x^2$

$4\pi x$

$4\pi^2 x^2$

$4\pi + \pi x^2$

Explanation

Write the formula to find the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (2x)^2 = 4\pi x^2$

9

The diameter of a circle is . Give the area of the circle in terms of .

Explanation

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle and $\pi$ is approximately .

$Area=\frac{\pi (4t)^2}{4}=\frac{16\pi t^2}{4}=4\pi t^2 \Rightarrow Area\approx 4\times 3.14\times t^2$

$\Rightarrow Area\approx 12.56t^2$

10

What is the area of a circle with a diameter equal to 6?

$9\pi$

$3\pi$

$18\pi$

$36\pi$

Explanation

First, solve for radius:

$r=\frac{d}{2}=\frac{6}{2}=3$

Then, solve for area:

$A=r^2\pi=3^2\pi=9\pi$

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