find the area of each triangle.
1.
2. 10 in.
3. 10 yd
7 m 15 in. 16 yd

find the length of each base. the area is given.
4.
5. 5 m
6. 17 ft
a = 500 cm² a = 45 m² a = 68 ft²

Question

find the area of each triangle.
1.
2. 10 in.
3. 10 yd
7 m 15 in. 16 yd

find the length of each base. the area is given.
4.
5. 5 m
6. 17 ft
a = 500 cm² a = 45 m² a = 68 ft²

Accepted Answer

### Problem 1: Find the area of the triangle with base $ 7 \, \text{m} $ and height $ 4 \, \text{m} $
# Explanation:
## Step 1: Recall the formula for the area of a triangle
The formula for the area $ A $ of a triangle is $ A = \frac{1}{2} \times \text{base} \times \text{height} $.

## Step 2: Substitute the given values into the formula
Here, the base $ b = 7 \, \text{m} $ and the height $ h = 4 \, \text{m} $. Substituting these values, we get:
$$
A = \frac{1}{2} \times 7 \times 4
$$

## Step 3: Calculate the area
First, multiply $ 7 $ and $ 4 $: $ 7 \times 4 = 28 $. Then, multiply by $ \frac{1}{2} $: $ \frac{1}{2} \times 28 = 14 $.

# Answer:
The area of the triangle is $ 14 \, \text{m}^2 $.

### Problem 2: Find the area of the triangle with base $ 15 \, \text{in} $ and height $ 10 \, \text{in} $
# Explanation:
## Step 1: Recall the formula for the area of a triangle
The formula for the area $ A $ of a triangle is $ A = \frac{1}{2} \times \text{base} \times \text{height} $.

## Step 2: Substitute the given values into the formula
Here, the base $ b = 15 \, \text{in} $ and the height $ h = 10 \, \text{in} $. Substituting these values, we get:
$$
A = \frac{1}{2} \times 15 \times 10
$$

## Step 3: Calculate the area
First, multiply $ 15 $ and $ 10 $: $ 15 \times 10 = 150 $. Then, multiply by $ \frac{1}{2} $: $ \frac{1}{2} \times 150 = 75 $.

# Answer:
The area of the triangle is $ 75 \, \text{in}^2 $.

### Problem 3: Find the area of the triangle with base $ 16 \, \text{yd} $ and height $ 10 \, \text{yd} $
# Explanation:
## Step 1: Recall the formula for the area of a triangle
The formula for the area $ A $ of a triangle is $ A = \frac{1}{2} \times \text{base} \times \text{height} $.

## Step 2: Substitute the given values into the formula
Here, the base $ b = 16 \, \text{yd} $ and the height $ h = 10 \, \text{yd} $. Substituting these values, we get:
$$
A = \frac{1}{2} \times 16 \times 10
$$

## Step 3: Calculate the area
First, multiply $ 16 $ and $ 10 $: $ 16 \times 10 = 160 $. Then, multiply by $ \frac{1}{2} $: $ \frac{1}{2} \times 160 = 80 $.

# Answer:
The area of the triangle is $ 80 \, \text{yd}^2 $.

### Problem 4: Find the length of the base of a triangle with area $ 500 \, \text{cm}^2 $ and height $ 20 \, \text{cm} $
# Explanation:
## Step 1: Recall the formula for the area of a triangle
The formula for the area $ A $ of a triangle is $ A = \frac{1}{2} \times \text{base} \times \text{height} $. We need to solve for the base $ b $.

## Step 2: Rearrange the formula to solve for $ b $
Starting with $ A = \frac{1}{2} \times b \times h $, multiply both sides by $ 2 $ to get $ 2A = b \times h $. Then, divide both sides by $ h $ to get $ b = \frac{2A}{h} $.

## Step 3: Substitute the given values into the formula
Here, $ A = 500 \, \text{cm}^2 $ and $ h = 20 \, \text{cm} $. Substituting these values, we get:
$$
b = \frac{2 \times 500}{20}
$$

## Step 4: Calculate the base
First, multiply $ 2 $ and $ 500 $: $ 2 \times 500 = 1000 $. Then, divide by $ 20 $: $ \frac{1000}{20} = 50 $.

# Answer:
The length of the base is $ 50 \, \text{cm} $.

### Problem 5: Find the length of the base of a triangle with area $ 45 \, \text{m}^2 $ and height $ 5 \, \text{m} $
# Explanation:
## Step 1: Recall the formula for the area of a triangle
The formula for the area $ A $ of a triangle is $ A = \frac{1}{2} \times \text{base} \times \text{height} $. We need to solve for the base $ b $.

## Step 2: Rearrange the formula to solve for $ b $
Starting with $ A = \frac{1}{2} \times b \times h $, multiply both sides by $ 2 $ to get $ 2A = b \times h $. Then, divide both sides by $ h $ to get $ b = \frac{2A}{h} $.

## Step 3: Substitute the given values into the formula
Here, $ A = 45 \, \text{m}^2 $ and $ h = 5 \, \text{m} $. Substituting these values, we get:
$$
b = \frac{2 \times 45}{5}
$$

## Step 4: Calculate the base
First, multiply $ 2 $ and $ 45 $: $ 2 \times 45 = 90 $. Then, divide by $ 5 $: $ \frac{90}{5} = 18 $.

# Answer:
The length of the base is $ 18 \, \text{m} $.

### Problem 6: Find the length of the base of a triangle with area $ 68 \, \text{ft}^2 $ and height $ 17 \, \text{ft} $
# Explanation:
## Step 1: Recall the formula for the area of a triangle
The formula for the area $ A $ of a triangle is $ A = \frac{1}{2} \times \text{base} \times \text{height} $. We need to solve for the base $ b $.

## Step 2: Rearrange the formula to solve for $ b $
Starting with $ A = \frac{1}{2} \times b \times h $, multiply both sides by $ 2 $ to get $ 2A = b \times h $. Then, divide both sides by $ h $ to get $ b = \frac{2A}{h} $.

## Step 3: Substitute the given values into the formula
Here, $ A = 68 \, \text{ft}^2 $ and $ h = 17 \, \text{ft} $. Substituting these values, we get:
$$
b = \frac{2 \times 68}{17}
$$

## Step 4: Calculate the base
First, multiply $ 2 $ and $ 68 $: $ 2 \times 68 = 136 $. Then, divide by $ 17 $: $ \frac{136}{17} = 8 $.

# Answer:
The length of the base is $ 8 \, \text{ft} $.

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QUESTION IMAGE

Question

Explanation:

Problem 1: Find the area of the triangle with base \( 7 \, \text{m} \) and height \( 4 \, \text{m} \)

Step 1: Recall the formula for the area of a triangle

Step 2: Substitute the given values into the formula

Step 3: Calculate the area

Step 1: Recall the formula for the area of a triangle

Step 2: Substitute the given values into the formula

Step 3: Calculate the area

Step 1: Recall the formula for the area of a triangle

Step 2: Substitute the given values into the formula

Step 3: Calculate the area

Answer:

Problem 2: Find the area of the triangle with base \( 15 \, \text{in} \) and height \( 10 \, \text{in} \)