What is the area of the figure?

Understand the Problem

The question is asking to calculate the area of a composite figure given its dimensions. The figure consists of several rectangles, and the total area can be found by breaking it down into individual areas and summing them up.

Answer

$252 \, \text{in}^2$

Steps to Solve

Identify the Dimensions Break the composite figure into smaller rectangles and identify their dimensions.
- Rectangle 1 (top): Length = 12 in, Height = 15 in
- Rectangle 2 (middle): Length = 9 in, Height = 6 in
- Rectangle 3 (bottom): Length = 3 in, Height = 6 in
Calculate the Area of Each Rectangle Use the formula for the area of a rectangle, which is given by $A = \text{Length} \times \text{Height}$.
- Area of Rectangle 1: $$ A_1 = 12 , \text{in} \times 15 , \text{in} = 180 , \text{in}^2 $$
- Area of Rectangle 2: $$ A_2 = 9 , \text{in} \times 6 , \text{in} = 54 , \text{in}^2 $$
- Area of Rectangle 3: $$ A_3 = 3 , \text{in} \times 6 , \text{in} = 18 , \text{in}^2 $$
Sum the Areas of Each Rectangle Add the areas calculated for each rectangle to get the total area of the composite figure.

$$ \text{Total Area} = A_1 + A_2 + A_3 $$ $$ \text{Total Area} = 180 , \text{in}^2 + 54 , \text{in}^2 + 18 , \text{in}^2 $$
Calculate the Final Area Perform the addition to find the total area.

$$ \text{Total Area} = 180 + 54 + 18 = 252 , \text{in}^2 $$

The area of the figure is $252 , \text{in}^2$.

More Information

The area calculation involves breaking down a composite figure into simpler parts to make the measurement easier. By calculating the area of each rectangle and summing them up, we ensure that no section is overlooked.

Tips

Miscalculating the dimensions of each rectangle. Ensure you double-check the measurements before applying them in the area formula.
Forgetting to sum all areas after calculating them individually. Always perform the addition carefully.

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