Question

The triangle and the trapezoid share a 15 inch base and height of 10 inches.

The area of the trapezoid is less than twice the area of the triangle. Find the value of x. Explain your reasoning.





Can the area of the trapezoid be exactly twice the area of the triangle? Explain your reasoning.

Answer 1

15 ; yes

Explanation:

Base = 15 inches

Height = 10 inches

Area of triangle = 1/2* base * height

Area of triangle = 0.5 * 15 * 10

Area of triangle = 75 in²

Area of trapezium < 2(75)

Area of trapezium, A

A = 1/2*(x+b)h

x = top base ; b = bottom base ; h = 10

1/2*(x + 15)10 < 150

5x + 75 < 150

5x < 150 - 75

5x < 75

x < 15

Hence, Area of trapezoid :

A = 1/2 * (15 + 15)10

A = 1/2 * (30)10

A = 1/2 * 300

A = 150

Hence, Area of trapezium can be twice the area of triangle.

2(75) = 150