A family is building a rectangular fountain in the backyard. The yard is also rectangular and measures 6x by 7x. The fountain is going to measure 2x by 4x. Once the fountain is built, what will be the area of the remaining yard?
Please do not just give me the answers!! Can someone explain what I need to do to get an answer?
To find the area of the remaining yard, you need to subtract the area of the fountain from the total area of the yard. Here's how you can calculate it step by step:
1. Determine the total area of the yard:
- The yard is rectangular, so you can calculate its area by multiplying the length (6x) by the width (7x).
- The equation for the area of a rectangle is A = length × width.
- In this case, the area of the yard is A = 6x × 7x = 42x^2.
2. Determine the area of the fountain:
- The fountain is also rectangular, with a length of 2x and a width of 4x.
- The area of the fountain is A = length × width = 2x × 4x = 8x^2.
3. Calculate the area of the remaining yard:
- To find the area of the remaining yard, subtract the area of the fountain from the total area of the yard.
- The equation for the remaining area is A_remaining = A_yard - A_fountain.
- Substituting the values we calculated earlier, A_remaining = 42x^2 - 8x^2.
4. Simplify the equation:
- To simplify the equation, subtract 8x^2 from 42x^2: A_remaining = 34x^2.
The resulting expression, 34x^2, represents the area of the remaining yard.
find area of total original yard (length times width)
find area of fountain (its length times its width)
subtract the fountain area from the original yard area.