Question

In a Pentagon ABCDE DP is drawn perpendicular to AB and is perpendicular to CE also at point Q. If AP=BP=12 and EQ=CQ=8, DE=DC=10, DP=18, find the area of the Pentagon

Answer 1

a^2+b^2=c^2
a^2+8^2=10^2
a^2=10^2-8^2
a^2=36
a=6
Since there are two triangles that measure 6 and 8 their area together would be 6×8=48^2
There are two rectangles that measure the 12×8=192^2
There are two triangles at the base that measure 4×12=48^2
Total area= 48+48+192=288^2 units.