Question: What is the area of this figure? [Image description: A geometric figure with the following…

What is the area of this figure?

[Image description: A geometric figure with the following dimensions:

• 15 ft on the top side
• 3 ft on the right side
• 4 ft on the bottom right side
• 2 ft on the bottom middle side
• 3 ft on the bottom left side
• 4 ft on the left side
• 9 ft on the top left side
• 8 ft on the bottom side]

The figure is a combination of rectangles and right-angled triangles.

Solution

To find the area of the given figure, we can break it down into smaller rectangles and then sum their areas. 1. First, let’s identify the dimensions of the large rectangle at the top. The large rectangle has a length of 15 ft and a height of 9 ft. 2. Calculate the area of the large rectangle. \[ \text{Area}{\text{large\ rectangle}} = 15 \times 9 = 135 \text{ ft}^2 \] 3. Next, we’ll identify and subtract the areas of the two smaller rectangles at the bottom right and below to get the net area. 4. Identify the first smaller rectangle (bottom right). It has a length of 4 ft and a height of 4 ft. 5. Calculate the area of the first smaller rectangle. \[ \text{Area}{\text{small\ rectangle\ 1}} = 4 \times 4 = 16 \text{ ft}^2 \] 6. Identify the second smaller rectangle (bottom left). It has a length of 8 ft and a height of 3 ft. 7. Calculate the area of the second smaller rectangle. \[ \text{Area}{\text{small\ rectangle\ 2}} = 8 \times 3 = 24 \text{ ft}^2 \] 8. Subtract the areas of the smaller rectangles from the area of the large rectangle. \[ \text{Total\ Area} = \text{Area}{\text{large\ rectangle}} - \text{Area}{\text{small\ rectangle\ 1}} - \text{Area}{\text{small\ rectangle\ 2}} \] \[ \text{Total\ Area} = 135 - 16 - 24 = 95 \text{ ft}^2 \] Therefore, the area of the figure is \(95 \text{ ft}^2\).