Question

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13. ABCDE is a pentagon of which side BC is parallel to diagonal AD, EP is perpendicular
BC and EP intersects AD at the point Q. BC = 7cm, AD = 13cm, PE = 9cm. and it
PQ = PE, let us write by calculating the area of ABCDE in shape of pentagon
Lengt
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Answer 1

Answer:

72.5 cm2

Step-by-step explanation:

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,PQ=4/9 PE

PQ=4/9*9=4 cm

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=1/2*sum of parallel sides × Height

⇒ area(trapezium ABCD)

=1/2*(AD+BC)*PQ

=1/2*(13+7)*4=40cm2

Also,

Area of triangle

=1/2*base*height

⇒area(∆AED)=1/2*EQ*AD

⇒area(∆AED)=1/2*5*13=32.5 cm2

⇒ area(ABCDE) = 40 + 32.5 = 72.5 cm2