Problema Solution
A new dam being built has the shape of a trapezoid. The length of the base at the bottom of the dam is 2 times the height. The length of the base at the top of the dam is 1/5 times the height minus 30 feet.
a. Write an expression to find the area of the trapezoidal cross section of the dam.
b. If the height of the dam is 180 feet, find the area of this cross section.
Answer provided by our tutors
let
a = the length of the base at the bottom
b = the length of the base at the top
h = the height of the dam
the length of the base at the bottom of the dam is 2 times the height
a = 2h
the length of the base at the top of the dam is 1/5 times the height minus 30 feet
b = (1/5)h - 30
a) Write a expression to find the area of the trapezoid cross section of the dam
A = (1/2)(a + b)h
A = (1/2)(2h + (1/5)h - 30 )h
by simplifying we get
A = (1/10)(11h - 150)h
click here to see the step by step simplification
b. If the height if the dam is 180 feet, find the area of this cross section
h = 180 ft
A = (1/10)(11*150 - 150)*150
A = 22,500 ft^2
click here to see the step by step solution
the area of this cross section is 22,500 square feet.