Question

A figure is composed of a semicircle and a right triangle. Determine the area of the shaded region. Use 3.14 for π and round to the nearest tenth. Show all of your work.
(semicircle then the right triangle with 5 ft on the top and 4 ft on the bottom of the triangle)

I'm having trouble with this one. I need help figuring out how to solve this

Answer 1

If I am seeing the shape correctly the 4 and 5 are the legs of the triangle then you need to use the Pythagorean Theorem c^2 = 5^2 + 4^2 to find the length of the hypotenuse of the triangle (which is the diameter of the semi-circle).
But perhaps without a diagram I am missing something ??

Answer 2

I would show the diagram if I could but there's a line that goes straight up and another line that goes down at an angle (5 ft) and then the bottom that connects the two (4 ft). I describes it as best as I could so would I still use that same theorem?

Answer 3

Assuming we have a 3-4-5 rt. triangle. radius = 4/2 = 2.
A1 = (bh)/2 = (4*3)/2 = 6 Ft^2 = area of triangle.
A2 = shaded area.
A3 = (pi*r^2)/2 = (3.14*2^2)/2 = 6.28 Ft^2 = area of semi-circle.

A1 + A2 = A3
A2 = A3-A1 = 6.28 - 6 = 0.3 Ft^2.

Answer 4

Find the perimeter and area of the figure. Round your answer to the nearest hundredth, if necessary.

Composite shape formed by a semicircle and a right triangle. The base of the triangle is aligned with the radius of the semicircle. The triangle has a height of 4 centimeters and hypotenuse of 5 centimeters. The semicircle has a radius of 3 centimeters.