Question

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

Answer 1

The area of the poster is B. 535.5 in².

Step-by-step 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 $=\frac{3}{4} ( \pi r^{2} ).$

Here r = a = 10 inches.

So the area of the circle $=\frac{3}{4} ((3.1415) (10^{2}) ) = 235.6125.$

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.