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]]>#1. Solve the triangle with the Pythagorean theorem: a^2 + 12^2 = 13^2, a = 5. Find the area of the triangle: (5 x 12)/2 = 30. Multiply 30 by 2 because there are two triangles. The area of the rectangle is 60.
#2. Use the Pythagorean theorem to solve the triangle: 12^2 + b^2 = 15^2, get 9. Solve for the area: (12 x 9)/2 = 54. The rectangle's missing side length is 19 because the triangle's side is 9, 9 + 10 = 19, use to solve for area. 8 x 19 = 152. Add together to get 206, which is the area of the whole polygon.
Thanks!
]]>Assuming that's a rectangle then you can use Pythagoras to work out the height. Then it's just base x height.
Number 2:
Call the point where the 8 and 10 meet, point A, and the point where 10 and 15 meet point B. Extend AB until the line meets the 20 line, at point C. AC splits the polygon into a rectangle and a right angled triangle. But you need to calculate the lengths AB and BC.
You can get BC using Pythag again and that will allow you to calculate the length and width of the rectangle and the base and height for the triangle.
Bob
]]>Answers coming up, stay on line please.
Bob
]]>#1: https://i.imgur.com/4PIIUjw.png
#2: https://i.imgur.com/rdP6UPM.png