A countertop is in the shape of a trapezoid. The lengths of the bases are 70.5 and 65.5 inches long. The area of the countertop is 1224 square inches. Write and solve and equation to find the height of the countertop.​

18.

Step-by-step explanation:

We know that the formula to find the height of a trapezoid is: ((a+b)/2)*h.

Using this, we'll get: 18, which is your answer. You can plug in the numbers if you want to confirm this.

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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

18.75 gallons

step-by-step explanation: