SOLUTION: Please help me solve the missing base of a trapezoid. The area is 780cm.The height is 8.The shorter base is 48 cm. Also,help me find the height of a triangle with area 85 1

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Question 189870: Please help me solve the missing base of a trapezoid.
The area is 780cm.The height is 8.The shorter base is 48 cm.

Also,help me find the height of a triangle with area 85 1/3 ft. and base is 10 2/3 ft.

THANKS!.
Answer by schrammbledeggs(41) (Show Source):
You can put this solution on YOUR website!
The formula for area of a trapezoid is:
Area = height ( (base1 + base2) / 2)

So let's plug in what we know:

780cm = 8( base1 + 48cm) / 2)

We can divide by 8 at first:

780/8 = (base1 + 48cm) /2
97.5cm = (base1 + 48cm) /2

Now we can multiply both sides by 2:
97.5cm *2 = (base1 + 48cm) / 2 *2
195cm = base 1 + 48 cm

Subtract 48cm from both sides:
195cm - 48cm = base1 + 48cm - 48cm
147cm = base1
:)

Now...area of a triangle:
A = 1/2 * b * h
Let's plug in what we're given after changing mixed numbers to improper fractions:
85 1/3 ft = 256/3 ft
10 2/3 ft = 32/3 ft

256/3 ft = 1/2 * 32/3 * h
256/3 ft = 32/6 * h

Multiply both sides by the reciprocal of 32/6...which is 6/32 to isolate h:
256/3 ft * 6/32 = 32/6 * h * 6/32
1536/96 ft = h
Reduced into lowest terms:
16 ft = h

:)