Question

the triangle and the trapezoid have the same base area. Base b2 is twice the area the length of b1. What are the lengths of the bases of the trapezoid? ​

Answer 1

b₁ = 7 cm, b₂ = 14 cm

Explanation:

The area (A) of the triangle is calculated as

A =
`(1)/(2)` bh ( b is the base and h the height )

Here b = 21 and h = 6, then

A = 0.5 × 21 × 6 = 63 cm²

The area (A) of a trapezoid is calculated as

A =
`(1)/(2)` h (b₁ + b₂ )

Here A = 63 ( same as triangle ), h = 6 and b₂ = 2b₁ , then

0.5 × 6 × (b₁ + 2b₁ ) = 63

3 × 3b₁ = 63

9b₁ = 63 ( divide both sides by 9 )

b₁ = 7

and b₂ = 2 × 7 = 14

The bases of the trapezoid are 7 cm and 14 cm

Answer 2

Answer: b₁ = 7 and b₂ = 14.

Triangle: base=21 cm, height=6cm

Trapezoid: height=6 cm, b1=?, b2=?

Triangle -> A=bh/2 -> A=63 (b is base and h is height)

Trapezoid -> A=[(b₁+b₂)/2)]h (b₁ and b₂ are bases and h is height)

Since they have the same area, the formula will be:

63=[(b₁+2(b₁))/2)]h

x=7