Find area and perimeter of the c shape with dimensions
7cm
5cm
5cm
5cm
5cm
7cm
18cm
To find the area and perimeter of the C-shaped figure, we'll need to break it down into separate shapes and add them up.
First, we can separate the shape into a rectangle and two semicircles:
Perimeter:
- The perimeter of the rectangle is: 2(7cm) + 18cm = 32cm
- The perimeter of each semicircle is half the circumference of a full circle with radius 5cm. The circumference of a circle is 2πr, so the circumference of these semicircles is πr = 5π. Therefore, the total perimeter added by the semicircles is: 2(5π) = 10π
- So the total perimeter of the C-shaped figure is: 32cm + 10π ≈ 62.85cm
Area:
- The area of the rectangle is: 7cm x 18cm = 126cm^2
- The area of each semicircle is half the area of a full circle with radius 5cm. The area of a circle is πr^2, so the area of each semicircle is 1/2(π(5cm)^2) = 39.27cm^2. Therefore, the total area added by the semicircles is: 2(39.27cm^2) = 78.54cm^2
- So the total area of the C-shaped figure is: 126cm^2 + 78.54cm^2 = 204.54cm^2
To find the area and perimeter of the C-shaped figure, we need to find the area and perimeter of each individual shape and then subtract the smaller shape from the larger shape.
Let's break down the C-shaped figure into two rectangles and one semicircle:
Rectangle 1:
Width = 7 cm
Length = 5 cm
Area1 = Width1 * Length1 = 7 cm * 5 cm = 35 cm²
Perimeter1 = 2 * (Width1 + Length1) = 2 * (7 cm + 5 cm) = 24 cm
Semicircle:
Radius = 5 cm
Area2 = 1/2 * π * r² = 1/2 * π * (5 cm)² = 1/2 * π * 25 cm² ≈ 39.27 cm²
Circumference2 = π * Diameter = π * (2 * 5 cm) ≈ 31.42 cm
Rectangle 2:
Width = 7 cm
Length = 18 cm
Area3 = Width3 * Length3 = 7 cm * 18 cm = 126 cm²
Perimeter3 = 2 * (Width3 + Length3) = 2 * (7 cm + 18 cm) = 50 cm
Now, let's calculate the total area and perimeter of the C-shaped figure:
Total Area = (Area1 - Area2) + Area3 = (35 cm² - 39.27 cm²) + 126 cm² ≈ 121.73 cm²
Total Perimeter = (Perimeter1 + Circumference2 + Perimeter3) = 24 cm + 31.42 cm + 50 cm ≈ 105.42 cm
Therefore, the area of the C-shaped figure is approximately 121.73 cm², and the perimeter is approximately 105.42 cm.