The vertical end of a trough has the following dimensions: width at top 4.4 ft., width at bottom 3.2 ft., depth 3.5 ft. Find the area of the end of the trough.
Well, well, looks like we have a trough connoisseur here! Don't worry, I've got just the joke to break the ice: Why did the math book look sad? Because it had too many problems. Okay, let's tackle your question now.
To find the area of the end of the trough, we need to treat it as a trapezoid. The formula for the area of a trapezoid is (a + b) * h / 2, where a and b are the lengths of the parallel sides, and h is the height.
In this case, the top width (a) is 4.4 ft, the bottom width (b) is 3.2 ft, and the height (h) is 3.5 ft. Plug those values into the formula, and you'll have the area. Math, it's always got your back, unlike that unreliable friend who's always late for everything.
Calculating the area of the end of the trough, we get:
(4.4 + 3.2) * 3.5 / 2 = 7.6 * 3.5 / 2 = 26.6 ft²
So, the area of the end of the trough is approximately 26.6 square feet. Voila! I hope my clownery didn't distract you from the calculations too much.
To find the area of the end of the trough, you can divide it into two shapes: a trapezoid and a rectangle.
1. Calculate the area of the trapezoid:
- Width at top = 4.4 ft
- Width at bottom = 3.2 ft
- Depth = 3.5 ft
The formula to find the area of a trapezoid is:
Area = (a + b) * h / 2
where a and b are the lengths of the parallel sides, and h is the height.
In this case, the parallel sides of the trapezoid are the widths at the top and bottom, and the height is the depth.
Area of the trapezoid = (4.4 + 3.2) * 3.5 / 2
2. Now, calculate the area of the rectangle:
- Width of the rectangle = width at the bottom = 3.2 ft
- Height of the rectangle = depth = 3.5 ft
Area of the rectangle = width * height
Combine the areas of the trapezoid and rectangle to find the total area of the end of the trough:
Total area = Area of the trapezoid + Area of the rectangle
To find the area of the end of the trough, we need to calculate the area of a trapezoid. The formula to find the area of a trapezoid is given by:
Area = (1/2) * (sum of parallel sides) * height
In this case, the two parallel sides of the trapezoid are the width at the top and bottom of the trough, and the height is the depth of the trough.
Given:
Width at the top = 4.4 ft
Width at the bottom = 3.2 ft
Depth = 3.5 ft
We can plug these values into the formula to find the area:
Area = (1/2) * (4.4 + 3.2) * 3.5
= (1/2) * 7.6 * 3.5
= 26.6 square feet
Therefore, the area of the end of the trough is 26.6 square feet.