Answer :
Answer:
The Area of quadrilateral ABCD is 36 cm²
Step-by-step explanation:
Given in the figure as :
ABD and BCD is a triangle
Length of sides of Δ ABD is:
AD = 3 cm
AB = 4 cm
BD = x = [tex]\sqrt{(AB)^{2}+ (AD)^{2}}[/tex]
Or, BD = [tex]\sqrt{(4)^{2}+ (3)^{2}}[/tex] = [tex]\sqrt{25}[/tex] = 5 cm
Length of sides of ΔCBD is :
BC = 13 cm
CD = 12 cm
Now By Heron's formula
Area of triangle ABD = [tex]\sqrt{s (s -a)(s-b) (s-c)}[/tex]
And s = [tex]\frac{AB + BD +DA}{2}[/tex]
Or, s = [tex]\frac{4 + 5 +3}{2}[/tex]
Or, s = 6 cm
∴ Area of triangle ABD = [tex]\sqrt{6 (6 -4)(6-5) (6-3)}[/tex]
Or, Area of triangle ABD = [tex]\sqrt{36}[/tex] = 6 cm²
Similarly The area of Triangle CBD = [tex]\sqrt{s (s -a)(s-b) (s-c)}[/tex]
And s = [tex]\frac{CB + BD +DC}{2}[/tex]
Or, s = [tex]\frac{13 + 5 +12}{2}[/tex]
Or, s = 15 cm
∴ Area of triangle CBD = [tex]\sqrt{15 (15 -13)(15-5) (15-12)}[/tex]
Or, Area of triangle CBD = [tex]\sqrt{900}[/tex] = 30 cm²
The Area of quadrilateral ABCD = Area Δ ABD + Area Δ CBD
Or,The Area of quadrilateral ABCD = 6 cm² + 30 cm² = 36 cm²
Hence The Area of quadrilateral ABCD is 36 cm² Answer