The perimeter of a figure is the length of its outer sides.
In this case, we need to find the perimeter of the semi-circle on the top and the highlighted sides of the two triangles at the bottom.
The perimeter of a semi-circle is given by the following formula:
Where r is the radius of the semi-circle.
The length of the missing sides of the triangles is given by the Pythagorean theorem, like this:
Where b and c are the lengths of the legs of the triangles.
By replacing 8 for r into the first formula, we get:
By replacing 8 for b and 15 for c into the second equation, we get:
Then, we just have to add up the perimeter of the semi-circle and the lengths of the mentioned sides, two times, because there are two triangles, like this:
Perimeter = 8π + 17 + 17 = 8π + 34
Then, the perimeter of figure a equals 8π + 34 meters
The area of this figure can be calculated by summing up the area of the semicircle and the area of the triangle, like this:
The area of the semi-cirlce (red shaded area) is given by the following formula:
The area of the triangle (yellow shaded area) is given by the following formula:
Where b is the length of the base and h is the height of the triangle.
By replacing 8 for r into the first formula, we get:
By replacing 15 for h and 16 for b ( 8 + 8) into the second formula, we get:
By adding the area of the semi-circle and the area of a triangle, we get:
Area = 32π + 120
Then, the area of the figure equals 32π + 120 square meters