Question: What is the area of this figure? [Image description: A blue figure with dimensions labeled as…

What is the area of this figure?

[Image description: A blue figure with dimensions labeled as follows:

• Top side: 14 km
• Right side: 2 km
• Bottom right side: 4 km
• Bottom side: 8 km
• Left side: 8 km
• Top left side: 2 km
• Middle left side: 4 km
• Middle right side: 2 km]

Solution

To find the area of the given compound figure, follow these steps: First, identify the overall dimensions of the figure. \[ \text{Bottom width} = 8\, \text{km} & \] \[ \text{Left height} = 8\, \text{km} & \] \[ \text{Top width} = 14\, \text{km} & \] Next, determine the additional dimensions on the right side. \[ \text{Two vertical segments} = 2\, \text{km each} & \] \[ \text{Horizontal segment between them} = 4\, \text{km} & \] Now, visualize the figure as a larger rectangle with a smaller rectangle removed from the upper right corner. Calculate the area of the larger rectangle. \[ \text{Width of larger rectangle} = 14\, \text{km} & \] \[ \text{Height of larger rectangle} = 8\, \text{km} & \] \[ \text{Area of larger rectangle} = 14 \times 8 = 112\, \text{km}^2 & \] Calculate the dimensions of the smaller rectangle that is removed. \[ \text{Width of smaller rectangle} = 14\, \text{km} - 8\, \text{km} = 6\, \text{km} & \] \[ \text{Height of smaller rectangle} = 8\, \text{km} - 2\, \text{km} - 2\, \text{km} = 4\, \text{km} & \] \[ \text{Area of smaller rectangle} = 6 \times 4 = 24\, \text{km}^2 & \] Subtract the area of the smaller rectangle from the area of the larger rectangle to find the area of the compound figure. \[ \text{Area of compound figure} = 112\, \text{km}^2 - 24\, \text{km}^2 = 88\, \text{km}^2 & \] Therefore, the area of the figure is \(88\, \text{km}^2\).