A large canal will have a cross-section in the shape of an isosceles trapezoid. The top will be twice as wide as the bottom, and the depth will be 8.00 m. Because of the cost of the building materials, the bottom and two slopes sides are to measure 14.0 m altogether. What is the area of the cross-section?
If the sloping sides measure x each, then the bottom is 14-2x.
So, the cross-section has area 1/2 (8) (14-2x + 2(14-2x))/2 = 12(7-x)
To find the area of the cross-section of the canal, we need to compute the sum of the areas of the two trapezoids that make up the isosceles trapezoid shape.
Let's label the dimensions:
Height of the trapezoid = 8.00 m
Width of the bottom base = x
Width of the top base = 2x
Length of the sloping sides = 14.0 m
The formula to calculate the area of a trapezoid is given by:
Area = (1/2) * (sum of the bases) * height
Now, let's calculate the area of the bottom trapezoid first:
Base1 = x
Base2 = x (since it's an isosceles trapezoid, the bases are equal)
Height = 8.00 m
Area1 = (1/2) * (x + x) * 8.00
= 4.00 * x * 8.00
= 32.00 * x
Next, let's calculate the area of the top trapezoid:
Base1 = 2x (twice as wide as the bottom)
Base2 = 2x (again, equal due to isosceles trapezoid)
Height = 8.00 m
Area2 = (1/2) * (2x + 2x) * 8.00
= 4.00 * 2x * 8.00
= 64.00 * x
Now, we need to find the value of x, which is the width of the bottom base.
x + x + 14.0 = 2x + 14.0 = 14.0 m (since the bottom and two slope sides together measure 14.0 m)
Simplifying the equation:
14.0 = 2x + 14.0
2x = 14.0 - 14.0
2x = 0
x = 0/2
x = 0
This means that the bottom base width is 0, which doesn't make sense for the canal's cross-section. There might be an error in the problem statement or the given information.
Without a valid value for x (width of the bottom base), we can't compute the areas of the trapezoids or the overall area of the cross-section.