Question

Ivy is building a new L-shaped desk for her room. She wants to make sure it is large enough to hold all her supplies. The dimensions of the desk, in feet, are shown in the diagram. What is the area of the desk?

Answer 1

Answer: the answer is C

Explanation:

Answer 2

1. The area of the larger rectangle (assuming the desk was not L-shaped):
`\( 8 \text{ ft} * 6 \text{ ft} = 48 \text{ square ft} \)`

2. The area of the smaller cut-out rectangle:

`\( 3 \text{ ft} * 2 \text{ ft} = 6 \text{ square ft} \)`

3. The total area of the L-shaped desk:

`\( 48 \text{ square ft} - 6 \text{ square ft} = 42 \text{ square ft} \)`

The image shows a diagram of an L-shaped desk with various lengths marked. To calculate the area of such a shape, we typically break it down into simpler shapes, calculate the area of each, and then sum those areas. The L-shape can be seen as a large rectangle minus a smaller rectangle that's been cut out.

The dimensions given are for an L-shaped desk. The overall length from left to right is 8 feet, the total height is 6 feet, the bottom left corner has a width of 5 feet, and the top right corner has a height of 2 feet. To find the area of the desk, we need to subtract the area of the smaller rectangle (the missing part) from the larger rectangle (the full size if the desk wasn't L-shaped).

Step-by-Step Calculation:

1. Calculate the area of the larger rectangle, which would be the area if the desk were not L-shaped:

`\( Area_(large) = length * width = 8 \text{ ft} * 6 \text{ ft} \)`

2. Calculate the area of the smaller cut-out rectangle:

`\( Area_(small) = length * width \)`

For the length, we subtract the length of the remaining bottom part from the total length:
`\( 8 \text{ ft} - 5 \text{ ft} = 3 \text{ ft} \).`

The width is given as the height of the upper right part of the L-shape:
`\( 2 \text{ ft} \).`

So,
`\( Area_(small) = 3 \text{ ft} * 2 \text{ ft} \)`

3. Subtract the area of the smaller rectangle from the area of the larger rectangle to find the total area of the L-shaped desk:

`\( Area_(desk) = Area_(large) - Area_(small) \)`

Let's perform these calculations.

The total area of the L-shaped desk is 42 square feet. Here's how we calculated it:

1. The area of the larger rectangle (assuming the desk was not L-shaped):

`\( 8 \text{ ft} * 6 \text{ ft} = 48 \text{ square ft} \)`

2. The area of the smaller cut-out rectangle:

`\( 3 \text{ ft} * 2 \text{ ft} = 6 \text{ square ft} \)`

3. The total area of the L-shaped desk:

`\( 48 \text{ square ft} - 6 \text{ square ft} = 42 \text{ square ft} \)`