The diagonals AC and EC of the pentagon forms two right triangles and
on isosceles triangle, together which gives the area of the pentagon.
Correct response:
- The area of the convex pentagon is <u>104 square units</u>.
The given parameters are;
AB = 5
BC = 12
AE = 13
DE = 8
CD = 6
m∠B = m∠D = 90°
Required:
The area of the convex pentagon ABCDE
Solution:
The area of pentagon ABCDE = Right ΔABC + Right ΔCDE + ΔACE
Area of right triangle ΔABC = × 5 × 12 = 30
Area of right triangle ΔCDE = × 6 × 8 = 24
Length of AC =
Which gives; AC = = 13
Length of EC =
Which gives; EC = = 10
Therefore, ΔACE is an isosceles triangle
Base of ΔACE = EC
Therefore;
Height of isosceles triangle ΔACE = = 12
Area of ΔACE = × 10 × 12 = 60
Therefore;
- Area of the convex pentagon ABCDE = 30 + 24 + 60 = <u>104</u>
Learn more about finding the area of geometric figures here: