# Find the Area of a Quadrilateral Abcd in Which Ad = 24 Cm, ∠Bad = 90° and Bcd Forms an Equilateral Triangle Whose Each Side is Equal to 26 Cm. (Take √3 = 1.73) - Mathematics

Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm. (Take √3 = 1.73)

#### Solution

Given that, a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90°
BCD is equilateral triangle and sides BC = CD = BD = 26 cm
In ΔBAD By using Pythagoras theorem

BA^2=BD^2-AD^2

⇒BA=sqrt(BD^2-AD^2)

=sqrt(676-576)

sqrt(100)=10cm

𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐵𝐴𝐷=1/2×𝐵𝐴×𝐴𝐷
=1/2×10×24
=120cm^2

𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐵𝐶𝐷=sqrt(a)/4xx(26)^2=292.37cm^2

∴𝐴𝑟𝑒𝑎 𝑜𝑓 𝑞𝑢𝑎𝑑𝑟𝑖𝑙𝑎𝑡𝑒𝑟𝑎𝑙
ABCD = Area of ΔBAD + area of ΔBCD
= 120 + 292.37
= 412.37 cm^2

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.2 | Q 7 | Page 20