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 104 square units.
Which is the methods used to finding the area of a pentagon
The area of the convex polygon is found by the sum of the
areas of the three triangles that are formed by drawing two
diagonals facing the two 90° angles.
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 = [tex]\frac{1}{2}[/tex] × 5 × 12 = 30
Area of right triangle ΔCDE = [tex]\frac{1}{2}[/tex] × 6 × 8 = 24
Length of AC = [tex]\mathbf{\sqrt{\overline{AB}^2 + \overline{BC}^2}}[/tex]
Which gives; AC = [tex]\mathbf{\sqrt{5^2 + 12^2}}[/tex] = 13
Length of EC = [tex]\mathbf{\sqrt{\overline{CD}^2+ \overline{DE}^2}}[/tex]
Which gives; EC = [tex]\mathbf{\sqrt{6^2 + 8^2}}[/tex] = 10
Therefore, ΔACE is an isosceles triangle
Base of ΔACE = EC
Therefore;
Height of isosceles triangle ΔACE = [tex]\mathbf{\sqrt{13^2 - 5^2}}[/tex] = 12
Area of ΔACE = [tex]\mathbf{\frac{1}{2}}[/tex] × 10 × 12 = 60
Therefore;
- Area of the convex pentagon ABCDE = 30 + 24 + 60 = 104
Learn more about finding the area of geometric figures here:
https://brainly.com/question/2279661
