Question

find the area of the figure. (sides meet at right angles.)

\\(\text{m}^2\\)

Explanation:

Decompose the composite figure

We divide the shape vertically into three simpler rectangles.

• Left rectangle: width \(5\text{ m}\), height \(7\text{ m}\).
• Right rectangle: width \(5\text{ m}\), height \(7\text{ m}\).
• Middle bottom rectangle: width \(3\text{ m}\).

Determine the middle height

The total height is \(7\text{ m}\).
The inner cutout depth is \(5\text{ m}\).
The height of the middle bottom section is:

$$ 7\text{ m} - 5\text{ m} = 2\text{ m} $$

Calculate individual areas

We find the area of each of the three decomposed parts.

• Left area:

$$ A_1 = 5\text{ m} \times 7\text{ m} = 35\text{ m}^2 $$

• Right area:

$$ A_2 = 5\text{ m} \times 7\text{ m} = 35\text{ m}^2 $$

• Middle area:

$$ A_3 = 3\text{ m} \times 2\text{ m} = 6\text{ m}^2 $$

Sum the areas

We add the three areas to find the total area.

$$ A_{\text{total}} = 35 + 35 + 6 = 76\text{ m}^2 $$

Answer:

Find the area of the figure. (Sides meet at right angles.)

<blank>76</blank> \(\text{m}^2\)