Problem G-1 Schyler Fennimore

B 9 12 Problem G-1: Let ABCDE be a convex pentagon whose sides measure as follows: AB = 9, BC = 12, CD = 5, DE = 12, and AE = 8. If the interior angles at B and D are right angles, compute the area of ABCDE. So first, I broke my pentagon up into 3 triangles. A C 8 5 D E 12

B 9 12 Area of ABC = ½bh = 54 54 Since ABC is a right triangle, you would use the formula, ½ bh to find the area of that triangle. ½ (9)(12) = 54 A C 8 5 D E 12

B 9 Area of EDC = ½bh = 30 12 54 Since EDC is a right triangle, you would use the formula, ½ bh to find the area of that triangle. ½ (5)(12) = 30 A C 8 5 30 D E 12

B 9 12 Find AC and EC Use the pathagorem theorem to find AC and EC. AC = 81+144 = 15 EC = 144+25 = 13 15 A C 8 5 13 D E 12

Now use Heron’s Theorem B 9 Now use Heron’s Theorem 12 54 𝑆= 15+13+8 2 =18 𝐴= 18 18−15 18−13 18−8 𝐴= 18∙3∙5∙10 =30 3 15 A C 30 3 8 5 13 30 D E 12

Add all 3 triangles together B 9 Add all 3 triangles together 12 54 54 + 30 + 30 3 = 84 + 30 3 15 A C 30 3 8 5 13 30 D E 12