CBSE Class 12-science Answered

Dear Student,

Let base length be x cm. Then:

Area = ½ × (Sum of parallel sides) × (distance between them)

=> A = ½ × (x+10) × 10sinӨ

=> A = 5sinӨ × (x+10)……………………………(1)

Also,

x- 2×10sinӨ = 10

=> 5sinӨ = (x-10)/4

On substituting it in equation (1), we get:

A = (x-10)/4 ×(x+10)

=> A = (x² - 100)/4…………………………(2)

For A to be maximum, dA/dx = 0

So,

2x-100 = 0

=> x = 50 cm

Substituting the value of x in equation (2),

A = (2500-100)/4

=> A = 2400/4

So Area of trapezium = 600 cm²