Find the Perimeter of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
To find the perimeter of the figure, we need to find the lengths of all sides and add them together.
First, let's find the length of side AB. This is the length of the rectangle and can be found using the Pythagorean theorem. The length of side AB can be calculated as the square root of the sum of the squares of the width (6) and the length of BC (8):
AB = √(6^2 + 8^2) = √(36 + 64) = √100 = 10
Next, let's find the length of the curved side BC. This is the circumference of the semicircle and can be calculated using the formula for the circumference of a circle, C = πd, where d is the diameter. The diameter of the semicircle is equal to the width of the rectangle, which is 6.
BC = πd = π(6) = 6π
Now, let's find the length of side CD. This is the length of the rectangle and is equal to the width, which is 8.
Finally, let's find the length of side DE. This is the opposite side of the curved side and is equal to the radius of the semicircle, which is half the width of the rectangle, 6.
DE = 6
To find the perimeter, we add all these lengths together:
Perimeter = AB + BC + CD + DE = 10 + 6π + 8 + 6
Rounded to the nearest tenth place, the perimeter of the figure is approximately:
Perimeter ≈ 10 + 6π + 8 + 6 ≈ 24 + 6π ≈ 24 + 6(3.14) ≈ 24 + 18.84 ≈ 42.8
Therefore, the perimeter of the figure, rounded to the nearest tenth place, is 42.8.