1. Problem G-1
Schyler Fennimore

2. 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

3. 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

4. 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

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

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

7. Add all 3 triangles togetherB 9
Add all 3 triangles together 12 54 = 15 A C
30 3 8 5 13 30 D E 12