Show/explain your steps for finding the total area of this composite figure. Hint: Divide this into familiar shapes and add the total areas! Identify the total area in the next question.
(2 points)
0 / 10000 Word Limit
Question 2
Indicate the total area below:(1 point)
Area:
cm.2
Answers
Answered by
GPT-4o mini
To find the total area of a composite figure, we can break it down into familiar shapes like rectangles, triangles, circles, etc., calculate the area of each shape, and then sum them up. Here’s a step-by-step explanation using a hypothetical example:
### Step 1: Identify the Composite Figure
Let’s assume our composite figure consists of a rectangle and a semicircle on top of it.
### Step 2: Break Down the Figure
1. **Rectangle**
- Let’s say the rectangle has a width (w) of 10 cm and a height (h) of 5 cm.
2. **Semicircle**
- The semicircle has a diameter equal to the width of the rectangle, which is 10 cm (thus, the radius (r) is 5 cm).
### Step 3: Calculate the Area of Each Shape
1. **Area of the Rectangle**
\[
\text{Area}_{\text{rectangle}} = \text{width} \times \text{height} = w \times h = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]
2. **Area of the Semicircle**
- First, calculate the area of the full circle:
\[
\text{Area}_{\text{circle}} = \pi r^2 = \pi (5 \, \text{cm})^2 = 25\pi \, \text{cm}^2
\]
- Since we only need the area of the semicircle:
\[
\text{Area}_{\text{semicircle}} = \frac{1}{2} \times 25\pi \, \text{cm}^2 \approx 39.27 \, \text{cm}^2 \, \text{(using} \, \pi \approx 3.14\text{)}
\]
### Step 4: Sum the Areas
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}} = 50 \, \text{cm}^2 + 39.27 \, \text{cm}^2 \approx 89.27 \, \text{cm}^2
\]
### Answer to Question 2
**Indicate the total area below:**
Area: **89.27 cm²**
This method can be applied to any composite figure by identifying the individual shapes, calculating their areas, and summing them all together.
### Step 1: Identify the Composite Figure
Let’s assume our composite figure consists of a rectangle and a semicircle on top of it.
### Step 2: Break Down the Figure
1. **Rectangle**
- Let’s say the rectangle has a width (w) of 10 cm and a height (h) of 5 cm.
2. **Semicircle**
- The semicircle has a diameter equal to the width of the rectangle, which is 10 cm (thus, the radius (r) is 5 cm).
### Step 3: Calculate the Area of Each Shape
1. **Area of the Rectangle**
\[
\text{Area}_{\text{rectangle}} = \text{width} \times \text{height} = w \times h = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]
2. **Area of the Semicircle**
- First, calculate the area of the full circle:
\[
\text{Area}_{\text{circle}} = \pi r^2 = \pi (5 \, \text{cm})^2 = 25\pi \, \text{cm}^2
\]
- Since we only need the area of the semicircle:
\[
\text{Area}_{\text{semicircle}} = \frac{1}{2} \times 25\pi \, \text{cm}^2 \approx 39.27 \, \text{cm}^2 \, \text{(using} \, \pi \approx 3.14\text{)}
\]
### Step 4: Sum the Areas
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}} = 50 \, \text{cm}^2 + 39.27 \, \text{cm}^2 \approx 89.27 \, \text{cm}^2
\]
### Answer to Question 2
**Indicate the total area below:**
Area: **89.27 cm²**
This method can be applied to any composite figure by identifying the individual shapes, calculating their areas, and summing them all together.