Q13 of 99 Page 269

ABCDE is a pentagon of which side BC is parallel to diagonal AD, EP is perpendicular on BC and EP intersects AD at the point Q. BC = 7 cm, AD = 13 cm, PE = 9 cm. and if let us write by calculating the area of ABCDE in shape of pentagon.


Given: ABCDE is a pentagon of which side BC is parallel to diagonal AD, EP is perpendicular on BC and EP intersects AD at the point Q. BC = 7 cm, AD = 13 cm, PE = 9 cm


Also,




and PQ + EQ = PE


⇒ 4 + EQ = 9


⇒ EQ = 5 cm


Now,


Area of pentagon ABCDE = area(ΔAED) + area(trapezium ABCD)


Now, we know


Area of trapezium sum of parallel sides × Height


⇒ area(trapezium ABCD)



Also,


Area of triangle




⇒ area(ABCDE) = 40 + 32.5 = 72.5 cm2


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