The area of trapezoid is h( b1+b2)/5,
where h is the altitude, and b1 and b2 are the lenghts of the parallel bases. If trapezoid has an altitude of 5 inches, an area of 55 square inches , and one base 12 inches long, what is the lenghth, in inches, of its other base?
Please for some sugesstions.
A=h( b1+b2)/2,
h=5
b=12
A=55
=>
55=5(12+b2)/2
Solve for b2.
To find the length of the other base of the trapezoid, we can use the given formula for the area of a trapezoid and substitute the known values.
Given:
Altitude (h) = 5 inches
Area = 55 square inches
Base 1 (b1) = 12 inches
The formula for the area of a trapezoid is A = (h * (b1 + b2)) / 2.
Substituting the given values, we have:
55 = (5 * (12 + b2)) / 2
To solve for b2, we can simplify the equation as follows:
Multiply both sides of the equation by 2 to eliminate the fraction:
110 = 5 * (12 + b2)
Distribute 5 on the right side of the equation:
110 = 60 + 5b2
Subtract 60 from both sides of the equation:
50 = 5b2
Divide both sides of the equation by 5 to isolate b2:
10 = b2
Therefore, the length of the other base (b2) is 10 inches.
To summarize, the suggested steps to find the length of the other base are:
1. Use the formula for the area of a trapezoid: A = (h * (b1 + b2)) / 2.
2. Substitute the given values into the formula: 55 = (5 * (12 + b2)) / 2.
3. Simplify the equation and solve for b2: 10 = b2.
Hence, the length of the other base is 10 inches.