Question 189870
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


:)