Question

A patio will be built in the shape of a trapezoid. The base of the trapezoid will measure 14.5 ft and 22.5 ft. What is the minimum height of the trapezoid if the patio is to have an area of no less than 259 sq ft

Answer 1

Hopefully this helps. I thought it would be better to just write it out rather than try to explain with words. If you don't understand something in the photo above I'm happy to explain

Answer 2

the minimum height of the trapezoid must be 14 feet

Explanation:

Hello

The area of ​​a trapezoid is calculated from its height and the two parallel sides (a and b) or bases of the trapezoid. It is the result of multiplying its height (h) and the median of the trapezoid, which is obtained as the average of the two bases a and b: M = (a + b) / 2

`A=(a+b)/(2)*h`

where A is the area, "a" is a base, "b" is the other base and "h" is the heigth

Step 1

we need to find the length, hence, le's isolate "h"

`A=(a+b)/(2)*h\\2A={(a+b)*h}\\ h=(2A)/((a+b))`

Step 2

put the values into the equation

Let

A=259 square feet

a=14.5 ft

b=22.5 ft

`h=(2A)/((a+b)) \\h=(2*259)/((14.5+22.5)) \\h=(518)/(37) \\h=14\ feet`

hence, the minimum height of the trapezoid must be 14 feet.

Have a great day