Question

find the area of the quadrilateral abcd in which ab = 3cm, bc = 4cm, cd = 4cm, da = 5cm and ac = 5cm

Answer 1

hey User !!

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here's your answer..

Area of Quadrilateral = Area of ∆ABC + Area of ∆ADC

Area of ∆ABC ::::------•

by using Heron's formula
$= \sqrt{s(s - a)(s - b)(s - c)} \\ \: \: s = \frac{a + b + c}{2} \\ = \frac{3 + 4 + 5}{2} = \frac{12}{2} = 6 \\ \\ ar \: of \: triangle \\ = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{6(6 - 3)(6 - 4)(6 - 5)} \\ = \sqrt{6 \times 6 } = 6 {cm}^{2}$
Area of ∆ADC :::::::-----•

by using Heron's formula
$s = \frac{a + b + c}{2} = \frac{5 + 4 + 5}{2} = \frac{14}{2} = 7 \\ \\ ar \: of \: triangle \: \\ = \sqrt{s(s - a)(s -b)(s - c) } \\ = \sqrt{7(7 - 5)(7 - 4)(7 - 5)} \\ = \sqrt{7 \times 2 \times 3 \times 2 } \\ = 2\sqrt{21} \\ = 2 \times 4.58 \\ = 9.16 {cm}^{2}$
Now ,

Area of Quadrilateral = ar of ∆ABC + ar of ∆ADC

$= (6 + 9.16) {cm}^{2} \\ = 15.16 {cm}^{2} \\ = 15.2 {cm}^{2} (approx.)$
so the Area of Quadrilateral ABCD is 15.2cm sq.