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Question

Find the area of the quadrilateral ABCD in which BCD is an equilateral triangle, each of whose sides is 26 cm, AD = 24 cm and ∠BAD = 90°. Also, find the perimeter of the quadrilateral. (Given: 3 = 1.73.)

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Solution

We know that BAD is a right-angled triangle.

AB=BD2-AD2=262-242=676-576=100=10 cm

Now,Area of triangle BAD=12×Base×Height = 12×AB×AD = 12×10×24 =120 cm2

Also, we know that BDC is an equilateral triangle.
Area of equilateral triangle = 34×(Side)2=34×(26)2=34×676=1693 =292.37 cm2

Now,
Area of quadrilateral ABCD = Area of ABD + Area of BDC
= (120 + 292.37) cm2 = 412.37 cm2
Perimeter of ABCD = AB + BC + CD + DA = 10 + 26+ 26 + 24 = 86 cm

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