Question

Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.

Answer 1

Explanation:

as the description says, the area is a rectangle (8×4) minus the half-circle at the right.

the radius of the (half-)circle is 4/2 = 2, as 4 is the diameter.

the area of the circle is

pi×r² = pi×2² = 4pi

the area of the half-circle is then

4pi/2 = 2pi

the area of the rectangle is

8×4 = 32

the total area is

32 - 2pi = 25.71681469... ≈ 25.7 square units

Answer 2

25.7 square units

Explanation:

You want the area of a 4 × 8 rectangle with a semicircle of diameter 4 removed from the end.

Area

The area of the enclosing rectangle is ...

A = LW

A = (8)(4) = 32 . . . . . square units

The are of the missing semicircle is ...

A = 1/2πr² . . . . . . where r is half the diameter

A = 1/2π(4/2)² = 2π ≈ 6.3 . . . . . square units

Then the area of the figure is ...

A = rectangle - semicircle = 32 -6.3 = 25.7 . . . . . square units

The area of the figure is about 25.7 square units.