Math, asked by akash0987, 1 year ago

find the area of a quadrilateral ABCD in which AB is equal to 3 cm,BC is equal to 4 cm, CD is equal to 4 cm, is equal to 5 cm, and AC is equal to 5 cm.

Answers

Answered by wishi
68
hey User !!

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•● •••------:::::::Question :::::::-----••• ●•

Find the area of a Quadrilateral ABCD in which AB=3cm, BC=4cm ,CD=4cm, DA=5cm and AC=5cm.


•••••• ::::::: SOLUTION ::::::::••••••

Area of Quadrilateral = Ar of ∆ABC + Ar 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)}  {cm}^{2}  \\  =  \sqrt{6 \times 3 \times 2 \times 1}  {cm}^{2}  \\   = \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}  \ {cm}^{2}  \\  = 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.

I hope
this helps
you.

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amrjeet93: hallo
Answered by lalitachoudhary1234
5

Answer:

thanks for your answer

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