Question

The height of a trapezoid can be expressed as (2x + 9) while the bases can be expressed as (3x - 7) and (x + 5). Write an expression to represent the area of the trapezoid

Answer 1

Given that,

The height of a trapezoid is (2x + 9).

The bases can be expressed as (3x - 7) and (x + 5).

To find,

An expression represent the area of the trapezoid.

Solution,

The formula for the area of trapezoid is given by :

$A=\dfrac{1}{2}(\text{sum of bases})\times \text{height}$

Put all the values,

$A=\dfrac{1}{2}(3x-7+x+5)\times (2x+9)\\\\=\dfrac{1}{2}(4x-2)\times (2x+9)\\\\=(2x-1)(2x+9)\\\\A=2x(2x)+9(2x)+(-1)(2x)+(-1)(9)\\\\=4x^2+18x-2x-9\\\\=4x^2+16x-9$

So, the area of the trapezoid will be $(4x^2+16x-9)\ \text{units}^2$