How do you calculate the area of a compound shape with an L-shape and a rectangle?

To calculate the area of a compound shape, split it into simpler shapes and sum their areas.

When dealing with a compound shape like an L-shape combined with a rectangle, the first step is to break the shape down into simpler, more manageable parts. Typically, you can divide the L-shape into two rectangles.

Start by identifying the dimensions of each rectangle. For the L-shape, you might have one vertical rectangle and one horizontal rectangle. Measure the length and width of each rectangle. For example, if the vertical rectangle has a length of 5 cm and a width of 3 cm, and the horizontal rectangle has a length of 7 cm and a width of 2 cm, you can calculate their areas separately.

The area of a rectangle is found by multiplying its length by its width. So, for the vertical rectangle, the area would be \(5 \text{ cm} \times 3 \text{ cm} = 15 \text{ cm}^2\). For the horizontal rectangle, the area would be \(7 \text{ cm} \times 2 \text{ cm} = 14 \text{ cm}^2\).

Next, add the areas of these two rectangles together to find the total area of the L-shape. In this example, the total area would be \(15 \text{ cm}^2 + 14 \text{ cm}^2 = 29 \text{ cm}^2\).

If you have an additional rectangle attached to the L-shape, calculate its area in the same way and add it to the total. For instance, if the attached rectangle has dimensions of 4 cm by 3 cm, its area would be \(4 \text{ cm} \times 3 \text{ cm} = 12 \text{ cm}^2\). Adding this to the previous total, the overall area would be \(29 \text{ cm}^2 + 12 \text{ cm}^2 = 41 \text{ cm}^2\).

By breaking the compound shape into simpler rectangles, calculating each area, and then summing them, you can easily find the total area of the compound shape.