Question

Solve the formula for b2.

Area of a trapezoid: A=12h(b1+b2)

Answer 1

A = (12h x b1) + (12h x b2)

A = 12hb1 + 12hb2

A - 12hb1 = 12hb1 - 12hb1 +12hb2

A - 12hb1 = 12hb2

(A - 12hb1) / (12h) = (12hb2) / (12h)

b2 = (A - 12hb1) / (12h)

Answer 2

b₂ =
`(2A-hb_(1) )/(h)`

Explanation:

A =
`(1)/(2)` h(b₁ + b₂) ← multiply both sides by 2 to clear the fraction

2A = h(b₁ + b₂) ← distribute

2A = hb₁ + hb₂ ( subtract hb₁ from both sides )

2A - hb₁ = hb₂ ( divide both sides by h )

`(2A-hb_(1) )/(h)` = b₂