Question

Piper cut the corner off a piece of wood to use for a project. What is the area, in square feet, of the piece of wood that is left? 5 ft 8 ft 2.5 ft 2.5 ft . ​

Answer 1

5(8) - (.5)(2.5)(2.5) = 40 - 3.125

= 36.875 square feet

Answer 2

The area of the piece of wood that is left is 36.875 square feet.

To calculate the area of the piece of wood after Piper cuts off the corner, we will:

1. Calculate the area of the original rectangle.

2. Calculate the area of the right triangle that was cut off.

3. Subtract the area of the triangle from the area of the rectangle to get the remaining area of the piece of wood.

Given:

- The original dimensions of the piece of wood are 8 ft by 5 ft.

- The cut-off corner forms a right triangle with legs of 2.5 ft each.

Here's how you calculate it:

Step 1: Calculate the area of the original rectangle.

`\[ \text{Area of rectangle} = \text{length} * \text{width} \]`

`\[ \text{Area of rectangle} = 8 \text{ ft} * 5 \text{ ft} \]`

`\[ \text{Area of rectangle} = 40 \text{ ft}^2 \]`

Step 2: Calculate the area of the right triangle.

`\[ \text{Area of triangle} = (1)/(2) * \text{base} * \text{height} \]`

`\[ \text{Area of triangle} = (1)/(2) * 2.5 \text{ ft} * 2.5 \text{ ft} \]`

`\[ \text{Area of triangle} = (1)/(2) * 6.25 \text{ ft}^2 \]`

`\[ \text{Area of triangle} = 3.125 \text{ ft}^2 \]`

Step 3: Subtract the area of the triangle from the area of the rectangle.

`\[ \text{Remaining area} = \text{Area of rectangle} - \text{Area of triangle} \]`

`\[ \text{Remaining area} = 40 \text{ ft}^2 - 3.125 \text{ ft}^2 \]`

`\[ \text{Remaining area} = 36.875 \text{ ft}^2 \]`