Determine the area of each composite
figure. The curve is a semicircle.
a)8 in.
5 in.
4 in and 2 in.
b)35 cm
10 cm
c)2.07 m
0.85 m
need help with this word problem . thanks as you provide solution
To find the area of a composite figure with a semicircle, you will need to break it down into separate shapes and calculate the area of each shape individually.
a) Let's start with the first figure. It consists of a semicircle and a rectangle.
1. Calculate the area of the semicircle:
The formula for the area of a semicircle is (πr^2)/2, where r is the radius of the semicircle. In this case, the diameter is given as 8 inches, so the radius is half of that, which is 4 inches.
Area of the semicircle = (π * 4^2)/2 = 8π square inches.
2. Calculate the area of the rectangle:
The dimensions of the rectangle are given as 5 inches and 4 inches.
Area of the rectangle = length * width = 5 inches * 4 inches = 20 square inches.
3. Add the areas of the semicircle and rectangle to get the total area:
Total area = Area of semicircle + Area of rectangle = 8π + 20 square inches.
b) Now let's move on to the second figure, which also consists of a semicircle and a rectangle.
1. Calculate the area of the semicircle:
The diameter is given as 35 cm, so the radius would be half of that, which is 17.5 cm.
Area of the semicircle = (π * 17.5^2) / 2 = 306.25π square cm.
2. Calculate the area of the rectangle:
The dimensions of the rectangle are given as 10 cm and 35 cm.
Area of the rectangle = length * width = 10 cm * 35 cm = 350 square cm.
3. Add the areas of the semicircle and rectangle to get the total area:
Total area = Area of semicircle + Area of rectangle = 306.25π + 350 square cm.
c) Finally, let's calculate the area of the third figure, which also consists of a semicircle and a rectangle.
1. Calculate the area of the semicircle:
The diameter is given as 2.07 m, so the radius would be half of that, which is 1.035 m.
Area of the semicircle = (π * 1.035^2) / 2 = 1.06585π square meters.
2. Calculate the area of the rectangle:
The dimensions of the rectangle are given as 0.85 m and 2.07 m.
Area of the rectangle = length * width = 0.85 m * 2.07 m = 1.7595 square meters.
3. Add the areas of the semicircle and rectangle to get the total area:
Total area = Area of semicircle + Area of rectangle = 1.06585π + 1.7595 square meters.
Note: If you would like the numerical value of the total areas, you can approximate the π value to 3.14 and perform the calculations.