Question

. Find the area of quadrilateral ABCD in which
AD = 24 cm, ZBAD = 90° and ABCD is an
equilateral triangle having each side equal to
26 cm. Also, find the perimeter of the
quadrilateral. [Given: 13 =1.73]​

Answer 1

Correct Question :

Find the area of quadrilateral ABCD in which AD = 24 cm, angle BAD = 90 degree and BCD is an equilateral triangle having each side equal to 26cm.Also, find the perimeter of the quadrilateral.

[Given: √3 = 1.73]

Solution:

Area of equilateral triangle BCD = (√3 /4) × side^2

= √3/4 × 26 × 26

= √3 × 13 × 13

= 169 √3

= 169 × 1.73

= 292.37 cm^2 .

In right angled ∆ ABD ,

(BD) ^2 = (AD) ^2 + (AB) ^2

(26) ^2 = (24) ^2 + (AB) ^2

(AB) ^2 = (26) ^2 - (24) ^2

(AB) ^2 = (26 + 24) - (26 - 24)

(AB) ^2 = 50 - 2

(AB) ^2 = 48

AB = √48

AB = 4 √3

AB = 4 × 1.73

AB = 6.92 cm

Area of right angled ∆ ABD =(1/2) × base × height

= 1/2 × 6.92 × 24

= 83.04 cm ^2

Area of quadrilateral =

area of ∆BCD + area of ∆ ABD

Area of quadrilateral = 292.37 + 83.04

Area of quadrilateral = 375.41 cm^2

Perimeter of the quadrilateral =

AB + BC + CD + DA

= 6.92 + 26 + 26 + 24

= 82.92 cm .