Find the area of the figure. (Sides meet at right angles.)
Understand the Problem
The question is asking to find the area of a geometric figure composed of different rectangles, with the sides meeting at right angles. To solve this, we need to calculate the area of each rectangle and then sum them up to get the total area.
Answer
The area of the figure is $61 \text{ yd}^2$.
Answer for screen readers
The area of the figure is $61 \text{ yd}^2$.
Steps to Solve
- Identify the dimensions of each rectangle
The given figure consists of several rectangles with the following dimensions:
- Rectangle 1: Width = $5 \text{ yd}$, Height = $3 \text{ yd}$
- Rectangle 2: Width = $2 \text{ yd}$, Height = $3 \text{ yd}$
- Rectangle 3: Width = $3 \text{ yd}$, Height = $3 \text{ yd}$
- Rectangle 4: Width = $5 \text{ yd}$, Height = $3 \text{ yd}$
- Rectangle 5: Width = $8 \text{ yd}$, Height = $2 \text{ yd}$
- Calculate the area of each rectangle
Use the formula for the area of a rectangle, which is given by $A = \text{width} \times \text{height}$.
-
Area of Rectangle 1: $$ A_1 = 5 \times 3 = 15 \text{ yd}^2 $$
-
Area of Rectangle 2: $$ A_2 = 2 \times 3 = 6 \text{ yd}^2 $$
-
Area of Rectangle 3: $$ A_3 = 3 \times 3 = 9 \text{ yd}^2 $$
-
Area of Rectangle 4: $$ A_4 = 5 \times 3 = 15 \text{ yd}^2 $$
-
Area of Rectangle 5: $$ A_5 = 8 \times 2 = 16 \text{ yd}^2 $$
- Sum the areas of all rectangles
Add the areas calculated for all rectangles to find the total area:
$$ A_{\text{total}} = A_1 + A_2 + A_3 + A_4 + A_5 $$
Substituting the values:
$$ A_{\text{total}} = 15 + 6 + 9 + 15 + 16 $$
- Calculate the final total area
Now calculate the sum:
$$ A_{\text{total}} = 61 \text{ yd}^2 $$
The area of the figure is $61 \text{ yd}^2$.
More Information
To find the area of composite geometric shapes, it’s essential to break the figure down into manageable rectangles or shapes, calculate the area of each one, and then sum them up for a total area. This method can be applied to various complex figures and is a fundamental skill in geometry.
Tips
- Forgetting to calculate the area for all parts of the composite figure.
- Adding incorrect values together, leading to an incorrect total.
- Misreading the dimensions of the rectangles, which can alter the area calculation.
AI-generated content may contain errors. Please verify critical information
