Question

Patty bought a "P" poster to put on her wall, as shown below.

3 a
Note: Figure is not drawn to scale
If a = 10 in, which of the following is closest to the area of the poster?
A.
354 in2
B. 535.5 in2
C.
614 in 2
D.
275.5 in?​

Answer 1

The area of the poster is B. 535.5 in².

Explanation:

Step 1:

The poster consists of a rectangle and three-quarters of a circle.

The rectangle has a length of a and width of 3a. The circle has a radius of a.

We calculate the areas of the individual shapes and sum them up to calculate the entire area of the poster.

Step 2:

The area of a rectangle is the product of its length and its width.

If a = 10 inches, the length is 10 inches and the width is 30 inches.

The area of the rectangle
`= (l)(w) = (10)(30)= 300.`

The area of the rectangle is 300 in².

Step 3:

The area of a circle
`= \pi r^(2) .` Here we only have three-quarters of a circle, so

The area of the given circle
`=(3)/(4) ( \pi r^(2) ).`

Here r = a = 10 inches.

So the area of the circle
`=(3)/(4) ((3.1415) (10^(2)) ) = 235.6125.`

The area of the circle is 235.6125 in².

Step 4:

The total area of the shape = The area of the rectangle + The area of the circle.

The total area of the shape
`= 300 + 235.6125 = 535.6125.`

So the area of the poster is B. 535.5 in².