Question

Find the area of the quadrilateral ABCD where AB = 8 m, BC = 15 m and CD = 13 m, DA = 12 m, m∠B = 90.

Answer 1

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Answer 2

Answer:

Area of quadrilateral is 157.76 cm^2.

Step-by-step explanation:

To find the area we have to divide the quadrilateral in two triangles of 90 degree.

So, now the area of triangle ABC will be 1/2*base*height.

1/2*8*15 = 80cm^2.

By using Pythagoras theorem we will get that (AC)^2 = AB^2 + BC^2.

AC^2 = 8^2 + 15^2.

On solving we will get the value of AC = 17cm.

Now, to find area of ADC by Henn's formulae we get.

Side s = a+b+c/2 = 12+17+13/2 = 21cm.

So, area =✓(s(s-a)(s-b)(s-c)).

Area= ✓(21(21-12)(21-17)(21-13)).

Which on solving we will get the area of ADC as 77.76cm^2.

So, the area of quadrilateral = 80 + 77.76 = 157.76cm^2.