Question

A window has the shape of a rectangle with a semi circle at the top. Find the approximate area of the window using the dimensions shown.

2ft by 4ft

Answer 1

First, let's find the area of the semi-circle.
Area of a circle = π*r²
Looking at the rectangle, the diameter for the circle is 2 ft. Since we need the radius though, divide the diameter by 2 to get the radius.
r = 1
A = π * 1²
A = π * 1
A = π

But since it's a semicircle, you need to divide that area by 2.
3.14/2 = 1.57

The area of the semi-circle is 1.57.

Area of a rectangle = lw
l = 2
w = 4
A = 2 * 4
A = 8

The area of the rectangle is 8.

Now add those together to get the area of the entire figure.

1.57 + 8 = 9.57

The figure is about 9.57 square feet.

Answer 2

The approximate area of the window is 9.57 ft²

The figure is a composite shape. Therefore, the area can be described as follows:

Area of the composite shape:

• area = area of semi circle + rectangle

area of a rectangle = lw = 4 × 2 = 8 ft²

area of the semi circle = 1 / 2 πr² = 1 / 2 × π × 1² = 1.57 ft²

Therefore,

area of the window = 8 + 1.57 = 9.57 ft²

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