Question 13 of 21
The drawing is composed of a rectangle and a semicircle. Find the area of the figure to the nearest unit.
A figure is composed of a rectangle and a semi-circle. The top edge of the rectangle measures 10 centimeters. The left edge measures 18 centimeters. The right edge of the rectangle is dashed and is also the diameter of the semi-circle.
Not drawn to scale.
A. 599 cm2
B. 217 cm2
C. 307 cm2
D. 689 cm
radius of semicircle = 18/2 = 9
area of semicircle = (1/2) pi (81) = about 127 cm^2
area of rectangle = 180 cm^2
so total= 307 cm^2
area = (10 * 18) + [π * (18/2)^2 * 1/2]
I will assume the semicircle is attached to the side of length 18 cm
which would make its radius 9 cm
total area = 1/2 circle + rectangle
= 1/2 (9^2(0)π + 10(18)
= 127.23... + 180
= 307 cm^2 to the nearest unit
To find the area of the figure, we need to find the area of the rectangle and the area of the semicircle, and then add them together.
The area of a rectangle is found by multiplying its length by its width. In this case, the length of the rectangle is 10 centimeters and the width is 18 centimeters. So the area of the rectangle is 10 cm * 18 cm = 180 cm².
The area of a semicircle is found by multiplying half the circumference of the semicircle by its radius. Since the right edge of the rectangle is also the diameter of the semicircle, the radius is half of the diameter, which is 18 centimeters / 2 = 9 centimeters. The circumference of the semicircle is half the circumference of a circle with the same diameter, so it is (pi * 18 cm) / 2 = 9π cm.
Now, we need to find half the circumference of the semicircle. This is done by dividing the circumference by 2, so half the circumference is 9π cm / 2 = (9/2)π cm.
The area of the semicircle is found by multiplying half the circumference by the radius. So the area of the semicircle is [(9/2)π cm] * 9 cm = (81/2)π cm².
Now, we can add the area of the rectangle and the area of the semicircle to get the total area of the figure:
Total area = area of rectangle + area of semicircle
Total area = 180 cm² + (81/2)π cm²
To get the answer in the nearest unit, we need to calculate the value of (81/2)π and round it to the nearest whole number. The value of pi is approximately 3.14.
(81/2) * 3.14 ≈ 127.155
So, the total area is approximately 180 cm² + 127 cm² = 307 cm².
Therefore, the answer is option C: 307 cm².