Question

Find the Area of the figure below, composed of a rectangle and a semicircle. The radius of the circle is shown. Round to the nearest tenths place.
6 is the rectangle
2 is the semicircle

Answer 1

To find the area of the figure composed of a rectangle and a semicircle, we can calculate the individual areas and then sum them up.

Area of the rectangle:
The rectangle has a length of 6 and a width equal to the diameter of the semicircle, which is 2 times the radius (2 × 2 = 4). Therefore, the area of the rectangle is length × width: 6 × 4 = 24 square units.

Area of the semicircle:
The semicircle has a radius of 2. The formula to calculate the area of a semicircle is (π × r^2) / 2, where r is the radius. Plugging in the values, we get (π × 2^2) / 2 = (π × 4) / 2 = 2π square units.

Total area of the figure:
To find the total area, we add the area of the rectangle and the area of the semicircle: 24 + 2π.

Now, to round the answer to the nearest tenth, we need to calculate the approximate value of π. Let's use 3.14 as an approximation.

Therefore, the total area is approximately 24 + 2 × 3.14 = 24 + 6.28 ≈ 30.28 square units.

Rounded to the nearest tenth, the area of the figure is approximately 30.3 square units.