Question

Write a polynomial expression to find the area ​

Answer 1

A = 2b² + 15b + 7

Explanation:

Assuming the figure is a trapezium , then

the area (A) is calculated as

A =
`(1)/(2)` h (b₁ + b₂)

where h is the perpendicular height between the parallel bases b₁ and b₂

here h = b + 7 , b₁ = 3b - 5 , b₂ = b + 7 , then

A =
`(1)/(2)` (b + 7)(3b - 5 + b + 7)

=
`(1)/(2)` (b + 7)(4b + 2) ← expand factors using FOIL

=
`(1)/(2)` (4b² + 30b + 14) ← distribute parenthesis by
`(1)/(2)`

= 2b² + 15b + 7