Question

Barb is making a banner that is shaped like a trapezoid the height of the banner is 24 inches the top of the banner is it 14 inches if the area of the banners 372 in.² what is the length of the bottom side

Answer 1

Answer:

The length of the bottom side of the banner is 17 in.

Step-by-step explanation:

Given,

Area of the Banner = $372\ in^2$

Height of the Banner = 24 in

Top side of the Banner = 14 in

We have to find the length of the bottom side of the banner.

Solution,

Let the length of the bottom side of the banner be 'x'.

Since the banner is in the shape of trapezoid.

So according to the formula of area of trapezoid, which is;

Area of trapezoid =$\frac{1}{2}\times \textrm{sum of parallel sides}\times \textrm{distance between them}$

Here top and bottom sides are parallel and distance between them is equal to the height of the banner.

Now substituting the values, we get;

$\frac{1}{2}\times24\times(x+14)=372\\\\12(x+14)=372\\\\x+14=\frac{372}{12}\\\\x+14=31\\\\x=31-14=17\ in$

Hence The length of the bottom side of the banner is 17 in.