Answer:
Explanation:
1. Find the area of the triangle.
The triangle is a right triangle so you can use the pythagorean theorem (a² + b² = c²).
It might be helpful to draw the line on the third side of the triangle to see it better.
The missing side is the hypotenuse, also c².
Plug in the values.
5² + 7² = c²
c² = 74
If you square root, c = √74 ≈ 8.6
However, we do not need to use this value to find the area of the triangle. Finding the hypotenuse is important for later steps.
To find the area of the triangle, we can use the formula A = 1/2bh
or A = 1/2(L)(W)
A = 1/2(5)(7)
A = 17.5
3. Find the area of the square.
Use the value from the previous step, 8.6 as the length for each side of the square (all four sides of a square are equal).
To find the area, multiply the length by the width.
A = L × W
Or use the formula A = S² since we know all sides of a square are equal.
A = 8.6 × 8.6 or
A = 8.6²
A = 73.96
4. Find the area of the semicircle.
To find the area of a circle, we use the formula A = πr²
To find the area of a semicircle, we will divide by half or multiply by 1/2.
A = 1/2πr²
Once again, we will use the value 8.6.
8.6 represents the diameter of the circle.
The diameter is double the radius, so we need to divide 8.6 by 2 to find the radius of the circle.
D = 2r
8.6 = 2r
r = 4.3
Plus the r value 4.3 into the previous formula for the semicircle.
A = 1.2π(4.3)²
A = 69.7
*Keep in mind these values are rounded so answer will not be exact.*
5. To find the combined area of the figure, add up the area of the triangle, square, and semicircle.
17.5 + 73.96 + 69.7 = 161.16
If you round to the nearest whole number, the area of the figure is 161 cm².
6. We already know the values for the sides of the triangle and square. To find the value for the semicircle, we can use the circumference formula (divided by 2 for a semicircle): C = 2πr --> C = πr
C = π(4.3)
C = 13.5
7. To find the perimeter of the entire shape, we will add up the value of all the sides.
5 + 7 + 8.6 + 8.6 + 13.5 = 42.7
If you round to the nearest whole number, the perimeter of the figure is 43 cm.