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Question

Find the area of the quadrilateral ABCD in which AD = 24 cm, BAD = 90o and Δ BCD is an equilateral triangle having each side equal to 26 cm. Also, find the perimeter of the quadrilateral. [Given, 3 = 1.73.]


Solution

ΔBDC is an equilateral triangle with side a = 26 cm

Area of ΔBDC  =3a24=3×2624=3×6764=292.37 cm2

By using Pythagoras theorem in the right-angled triangle ΔDAB, we get:

AD2+AB2=BD2242+AB2=262AB2=262242=6765762=100AB=10 cm

Area of ΔABD =12×base×height12×10×24=120 cm2

Area of the quadrilateral = Area of ΔBDC + Area of ΔABD 
=292.37+120=412.37 cm2

Perimeter of the quadrilateral =AB+AC+CD+AD=24+10+26+26=86 cm
 

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