Question

a carpenter cut a triangular piece from a rectangular wooden board as shown. what is the area, in square inches, of the wooden board after the triangle piece was removed

Answer 1

The area of the wooden board after the triangular piece was removed is
`\(72 \, \text{in}^2\).`

To determine the area of the wooden board after the triangular piece is removed, we need to calculate the area of the original rectangular board and then subtract the area of the removed triangle. The formula for the area of a rectangle is
`\( \text{Area} = \text{length} * \text{width} \),` and for a triangle, it is
`\( \text{Area} = (1)/(2) * \text{base} * \text{height} \).`

First, find the area of the rectangle using the given dimensions. Let's assume the length is ( L ) and the width is ( W ). In the illustration, it appears that the length is 12 inches, and the width is 8 inches. Therefore, the area of the rectangle
`(\( A_{\text{rectangle}} \)) is \( 12 * 8 = 96 \, \text{in}^2 \).`

Next, determine the area of the triangular piece that was removed. It seems the base is 8 inches (same as the width of the rectangle), and the height is 6 inches. Use the triangle area formula to find
`\( A_{\text{triangle}} = (1)/(2) * 8 * 6 = 24 \, \text{in}^2 \).`

Finally, subtract the area of the triangle from the area of the rectangle to find the area of the wooden board after the triangular piece was removed:

`\[ A_{\text{board}} = A_{\text{rectangle}} - A_{\text{triangle}} = 96 - 24 = 72 \, \text{in}^2 \].`

Therefore, the area of the wooden board after the triangular piece is removed is
`\( 72 \, \text{in}^2 \).`

Answer 2

Where is the shape of the borad

Explanation:

Anyways what u really do is find the area of the retangular wooden board and u find it by length times width. Then u find the area of the triangular piece by base times heigth divided by two and lst but not the least subtarc=act the area of the triangular piece from the area of the rectangukar wooden board.