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)
Answers
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