Question

14. The area of the quadrilateral is
4 cm
wo z
3 cm
5 cm
3 cm
4 cm
​

Answer 1

Answer:

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Answer 2

We have joined the AC to form two triangles so that the calculation of the area will be easy.

The area of the triangle ABC can be calculated by Heron's formula:

So, the semi-perimeter, where

a=3cm b=4cm c=5cm

s=a+b+c divide by 2

=3+4+5 divided by 2

=6cm

Heron's Formula for calculating the area:

A= √s(s-a) (s-b) (s-c)

=√6(6-3) (6-4) (6-5)

=√6(3) (2) (1)

And the sides of the triangle ACD are

a'=4cm

b'=5cm

c'=5cm

So, the semi-perimeter of the triangle:

a'+b'+c' divided by 2

=4+5+5 divided by 2

=14÷2

=7cm

Therefore, the area will be given by, Heron's formula

A= √s'(s'-a') (s'-b') (s'-c')

=√7(7-4) (7-5) (7-5)

=√7(7) (3) (2)

=2√21

=9.2cm²

Then, the total area of the quadrilateral will be:

Area of ∆ABC+ area

TOTAL AREA OF QUADRILATERAL ABCD

Hence, the area of the quadrilateral ABCD is

15.2cm