Question

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

Answer 1

Here is your solution

Given sides of quadrilateral

Ab = 3cm
Bc = 4cm
Cd = 4cm
Da = 5cm
Ac = 5cm

Firstly divide quadrilateral into two part:-

Triangle ABC and Triangle ADC

➡In triangle ABC

$Area \: of \: triangle \: abc = \frac{1}{2} \times b \times h \\ = \frac{1}{2 } \times 4 \times 3 \\ = 6cm {}^{2}$
Note :-Triangle ABC is right angle triangle it follow pythagoream thereom rule

➡In triangle ADC

firstly we find semi perimeter =a+ b+c/2
=5+5+4/2
=14/2
=7

$Area \: of \:scalene\: triangle \: adc \\ = \sqrt{s(s - a)(s - b)(s - c) } \\ = \sqrt{ 7(7 - 5)(7 - 5)(7 - 4) } \\ = \sqrt{7 \times 2 \times 2 \times 3 } \\ = 2 \sqrt{7 \times 3} \\ = 2 \sqrt{21} \\ = 9.16cm^2$
Note:-Triangle ADC is a scalene triangle so here we used heroine formula.

Now :-

Area of quadrilateral =area of triangle(ABC+ADC)
=(6+9.16)
=15.16cm^2

Hope it helps you