Find the area of the quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and ΔBCD is an equilateral triangle having each side equal to 26 cm. Also find the perimeter of the quadrilateral. [Give: √3 = 1.73.]

Question

Philoid · Accepted Answer

Given:

BC = 26 cm

DC = 26 cm

AD = 24 cm

BD = 26 cm

In ∆BCD,

= 292.37 cm²

In ∆ADB,

Base² + Perpendicular² = Hypotenuse²

⇒ AB² + AD² = DB²

⇒ AB² = DB² - AD²

⇒ AB² = 26² - 24²

⇒ AB² = 676 - 576

⇒ AB² = 100

⇒ AB= 10 cm

Area of ∆ADB = 1/2 × AB × AD

= 1/2 × 10 cm × 24 cm

= 120 cm²

Now,

Area of quadrilateral ABCD = Area of ∆ADB + Area of ∆BCD

= 120cm² + 292.37 cm²

= 412.37 cm²

And,

Perimeter of quadrilateral ABCD = AB + BC + CD + DA

= 10 cm + 26 cm + 26 cm + 24 cm

= 86 cm