Question

The composite figure below is a triangle and a semicircle. What is the exact area of the figure? Do NOT round at any point!

Answer 1

(2,3) and (-1,-5)
Distance =√(-1-2)^2 +(-5-3)^2
Distance  =√73 (diamter)
radius = (√73) / 2
 
area of semi-circle: 
= 1/2 πr^2
= 1/2  π ((√73) / 2)^2 
= 73 π / 8
= 9.125 π 

area of triangle:
= 1/2 (8)(3)
= 12

Area of the figure = area of semi-circle  + area of triangle

= 9.125π  + 12

answer
9.125π  + 12