A trapezoid has an area of 91 cm2. If the height is 13 cm and one side is 6 cm, what is the length of the other side?
By "side" I assume you mean one of the bases. If the other base is x, then we have
(6+x)/2 * 13 = 91
(6+x)/2 = 7
6+x = 14
x = 8
To find the length of the other side of the trapezoid, we can use the formula for the area of a trapezoid, which is (1/2) * (a + b) * h, where a and b are the lengths of the parallel sides and h is the height.
Given:
Area = 91 cm^2
Height (h) = 13 cm
Length of one side (a) = 6 cm
Let's substitute these values into the formula and solve for the length of the other side (b):
Area = (1/2) * (a + b) * h
91 = (1/2) * (6 + b) * 13
To simplify the equation, we can multiply both sides by 2:
182 = (6 + b) * 13
Next, distribute the 13 on the right side:
182 = 78 + 13b
Now, isolate the variable by subtracting 78 from both sides:
182 - 78 = 78 + 13b - 78
104 = 13b
Finally, divide both sides by 13 to solve for b:
104/13 = b
b = 8
Therefore, the length of the other side of the trapezoid is 8 cm.