MATH SOLVE

3 months ago

Q:
# Find the area of the triangles ABD and BCD using Heron’s formula. Hence find the area of quadrilateral ABCD.

Accepted Solution

A:

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 cmAB = 4 cmBD = 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 cmCD = 12 cmNow By Heron's formulaArea 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