For part A, we can find the perimeter of the shape by first adding up the lengths of the 1.2m side and two 1.8m sides.
1.2 + 1.8 * 2 = 4.8
Now, what about that curved part? It's simply a semi-circle. So, if we know the diameter, we know the circumference. Circumferences are the perimeter for circles.
If we then half the length of the circumference, we will find the perimeter of the curved part.
We get the circumference of a circle with this formula: C = [tex] \pi [/tex]d
We know the diameter is 1.2m and we can use 3.14 for [tex] \pi [/tex].
Plug in the values.
C = 3.14 * 1.2
C = 3.768
Add up 4.8 and 3.768.
4.8 + 3.768 = 8.568
Round to the nearest tenth.
8.568 ≈ 8.6
Now we have the perimeter.
Now for part B.
This section of the questions wants us to find the area of the shape.
If you look closely, you will see the shape is composed of two shapes that we know!
A rectangle and a semi-circle. If we add up the areas of both shapes, we will get the area for the shape.
To get the area of a rectangle, use this formula: Area = length * width
Plug in the values.
Area = 1.2 * 1.8
Area = 2.16
Now for the semi-circle part. We can get the area of a circle with this formula
A = [tex] \pi r^{2}[/tex]
We know that the diameter is 1.2 but we need the radius.
If you know the diameter, then you can get the radius by halving the diameter.
1.2 / 2 = 0.6
And we will use 3.14 for [tex] \pi [/tex].
Plug in the values.
A = 3.14 * 0.6^2
A = 3.14 * 0.36
A = 1.1304
And because we are dealing with a semi-circle, it is half of a regular circle.
So, the area of a semi-circle will be half of a full circle.
1.1304 / 2 = 0.5652
Add up 0.5652 and 2.16
0.5652 + 2.16 = 2.7252
Round to the nearest tenth.
2.7252 ≈ 2.8
So, the perimeter is 8.6 and the area is 2.8.
