Question

Find area of quadrilateral abcd in which AD =24cm angle BAC=90 and BCD forms Equilateral triangle Whose equal side is equal to 26cm (Take √3=1.73)

Answer 1

Answer:

The area of quadrilateral ABCD is 412.76 cm²

Step-by-step explanation:

Step 1 : Quadrilateral ABCD forms two triangles.

Equilateral triangle BCD with sides 26 cm and right angled triangle BAD with base 24 cm and hypotenuse 26 cm.

Step 2 : Using Pythagoras theorem get the height AB of the right angled triangle and the height of the Equilateral triangle.

AB = Square root of (BD² - AD²)

= Square root of (676 - 576)

= square root of 100 = 10 cm

Height of the Equilateral triangle :

Height = square root of (26² - (26/2)²)

= Square root of (507) = 22.52 cm

Step 3 : Calculate the area of the two triangles.

Area of a triangle = ½b × h

Area of the right angled triangle = ½ × 24 × 10 = 120 cm²

Area of the Equilateral triangle = ½ × 26 × 22.52 = 292.76 cm²

Step 4 : Sum the two areas to get the total area which is the area of quadrilateral ABCD.

292.76cm² + 120 cm² = 412.76 cm²