one base of a trapezoid is 10 ft. long, the altitude is 4 ft., and the area is 32 sq. ft. find the length of a line parallel to and 1 ft. above the 10-ft. base and included between the legs of the trapezoid.
The other base is 6
Since we want a line 1/4 of the way up the height, it will be 1/4 of the way from 10 to 6, or
10 - 1/4 (10-6) = 9
To find the length of a line parallel to the 10-ft base and 1 ft above it, included between the legs of the trapezoid, we can use the formula for the area of a trapezoid:
Area = (1/2) × (sum of the bases) × altitude
Given:
Base 1 = 10 ft
Altitude = 4 ft
Area = 32 sq. ft
Let's solve for the unknown base, which we'll call Base 2.
To rearrange the formula for the area of a trapezoid, we get:
32 = (1/2) × (10 + Base 2) × 4
Now, let's solve for Base 2:
Multiply both sides of the equation by 2 to get rid of the fraction:
2 × 32 = (10 + Base 2) × 4
64 = 40 + 4(Base 2)
Subtract 40 from both sides:
64 - 40 = 40 - 40 + 4(Base 2)
24 = 4(Base 2)
Divide both sides by 4 to isolate Base 2:
24 / 4 = (4(Base 2)) / 4
6 = Base 2
So the length of the line parallel to the 10-ft base and 1 ft above it, included between the legs of the trapezoid, is 6 ft.