Question

Find the area of quadrilateral ABCD whose sides are AB=13cm ,BC=12cm ,CD=9cm ,AD=14cm and diagonal BD=15cm

Answer 1

Answer:

138 cm²

Step-by-step explanation:

ABCD is an quadrilateral

Area of Quadrilateral ABCD  = Area of Δ ABD  + Area of Δ CBD

Δ ABD   AB = 13 cm BD = 15 cm AD = 14 cm

s = (13 + 15 + 14)/2  = 21

Area using Hero Formula

Area of Δ ABD = √(21)(21 - 13)(21 -14)(21-15)

= √21 * 8 * 7 * 6

= 84 cm²

Δ CBD   BC = 12 cm BD = 15 cm CD = 9 cm

s = (12 + 15 + 9)/2  = 18

Area using Hero Formula

Area of Δ CBD = √(18)(18 - 12)(18 -15)(18-9)

= √18 * 6 * 3 * 9

= 54 cm²

Area of Quadrilateral ABCD  = 84 + 54  =  138 cm²

Answer 2

Answer:

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