Question

find the area of the figure below using heron's formula, giving the answer to three decimal places. ​

Answer 1

Answer:

252 cm²(approx)

Step-by-step explanation:

Let the quadrilateral be ABCD.

In the figure, ΔABD is a right-angled triangle.

By Pythagoras Property,

Hypotenuse²=Base²+Altitude²

       Altitude²=Hypotenuse²-Base²

               AB²=AD²-BD²

               AB²=(20)²-(16)²                 [a²-b²=(a+b)(a-b)]

               AB²=(20+16)(20-16)

                 AB=√36×4

                 AB=√144

                 AB=12 cm

Then, Area of ΔABD= 1/2×12×16

          Area of ΔABD= 1/2×192

          Area of ΔABD= 96 cm²

In ΔBCD,(By Heron's Formula)

    s=20+23+16/2

    s=59/2=29.5 cm

A=√s(s-a)(s-b)(s-c)

  =√29.5×6.5×9.5×13.5

  =1/100√295×65×95×135

  =1/100√5×59×5×13×5×19×5×9×3

  =1/100×5×5×3√59×13×19×3

  =1/100×75×208.065024

  =1/4×3×208.065024

  =3×52.016256

  =156.048.........cm²

Total area of the quadilateral=96 cm+156.048.......cm²

Total area of the quadilateral=252cm²(approx)

This is the answer to your question.

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