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 [tex]= (l)(w) = (10)(30)= 300.[/tex]
The area of the rectangle is 300 in².
Step 3:
The area of a circle [tex]= \pi r^{2} .[/tex] Here we only have three-quarters of a circle, so
The area of the given circle [tex]=\frac{3}{4} ( \pi r^{2} ).[/tex]
Here r = a = 10 inches.
So the area of the circle [tex]=\frac{3}{4} ((3.1415) (10^{2}) ) = 235.6125.[/tex]
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 [tex]= 300 + 235.6125 = 535.6125.[/tex]
So the area of the poster is B. 535.5 in².
