find the area of each polygon.
1. square with side 8 m
2. rectangle with length 12 in and width 7 in
find the value of x in each polygon.
3. rectangle with height 2 m and area 16 m², solving for x (length)
4. square with area 144 ft², solving for x (side)
find the area of each parallelogram.
5. parallelogram with base 5 yd and height 10 yd
6. parallelogram with base 12 in and height 6 in
the area of each parallelogram is 120 ft². find the value of x in each parallelogram.
7. parallelogram with height 12 ft, solving for x (base)
8. parallelogram with height 6 ft, solving for x (base)
9. parallelogram with base 8 ft, solving for x (height)

Question

Accepted Answer

### Problem 1: Find the area of the square (8 m side)
# Explanation:
## Step1: Identify the formula for square area
The area of a square is given by $ A = s^2 $, where $ s $ is the side length.
## Step2: Substitute the side length
Here, $ s = 8 \, \text{m} $, so $ A = 8^2 $.
## Step3: Calculate the result
$ 8^2 = 64 $.
# Answer:
The area of the square is $ 64 \, \text{m}^2 $.

### Problem 2: Find the area of the rectangle (7 in by 12 in)
# Explanation:
## Step1: Recall the rectangle area formula
The area of a rectangle is $ A = l \times w $, where $ l $ is length and $ w $ is width.
## Step2: Substitute the values
Here, $ l = 12 \, \text{in} $ and $ w = 7 \, \text{in} $, so $ A = 12 \times 7 $.
## Step3: Compute the product
$ 12 \times 7 = 84 $.
# Answer:
The area of the rectangle is $ 84 \, \text{in}^2 $.

### Problem 3: Find $ x $ for the rectangle ($ A = 16 \, \text{m}^2 $, width = 2 m)
# Explanation:
## Step1: Use the rectangle area formula
$ A = l \times w $, so $ l = \frac{A}{w} $ (where $ l = x $, $ A = 16 $, $ w = 2 $).
## Step2: Substitute the values
$ x = \frac{16}{2} $.
## Step3: Perform the division
$ \frac{16}{2} = 8 $.
# Answer:
The value of $ x $ is $ 8 \, \text{m} $.

### Problem 4: Find $ x $ for the square ($ A = 144 \, \text{ft}^2 $)
# Explanation:
## Step1: Use the square area formula
$ A = x^2 $, so $ x = \sqrt{A} $.
## Step2: Substitute $ A = 144 $
$ x = \sqrt{144} $.
## Step3: Calculate the square root
$ \sqrt{144} = 12 $.
# Answer:
The value of $ x $ is $ 12 \, \text{ft} $.

### Problem 5: Find the area of the parallelogram (base = 5 yd, height = 10 yd)
# Explanation:
## Step1: Recall the parallelogram area formula
The area of a parallelogram is $ A = b \times h $, where $ b $ is base and $ h $ is height.
## Step2: Substitute the values
Here, $ b = 5 \, \text{yd} $ and $ h = 10 \, \text{yd} $, so $ A = 5 \times 10 $.
## Step3: Compute the product
$ 5 \times 10 = 50 $.
# Answer:
The area of the parallelogram is $ 50 \, \text{yd}^2 $.

### Problem 6: Find the area of the parallelogram (base = 12 in, height = 6 in)
# Explanation:
## Step1: Use the parallelogram area formula
$ A = b \times h $, with $ b = 12 \, \text{in} $ and $ h = 6 \, \text{in} $.
## Step2: Substitute and calculate
$ A = 12 \times 6 = 72 $.
# Answer:
The area of the parallelogram is $ 72 \, \text{in}^2 $.

### Problem 7: Find $ x $ for the parallelogram ($ A = 120 \, \text{ft}^2 $, height = 12 ft)
# Explanation:
## Step1: Use the parallelogram area formula
$ A = b \times h $, so $ b = \frac{A}{h} $ (where $ b = x $, $ A = 120 $, $ h = 12 $).
## Step2: Substitute the values
$ x = \frac{120}{12} $.
## Step3: Perform the division
$ \frac{120}{12} = 10 $.
# Answer:
The value of $ x $ is $ 10 \, \text{ft} $.

### Problem 8: Find $ x $ for the parallelogram ($ A = 120 \, \text{ft}^2 $, height = 6 ft)
# Explanation:
## Step1: Use the parallelogram area formula
$ A = b \times h $, so $ b = \frac{A}{h} $ (where $ b = x $, $ A = 120 $, $ h = 6 $).
## Step2: Substitute the values
$ x = \frac{120}{6} $.
## Step3: Perform the division
$ \frac{120}{6} = 20 $.
# Answer:
The value of $ x $ is $ 20 \, \text{ft} $.

### Problem 9: Find $ x $ for the parallelogram ($ A = 120 \, \text{ft}^2 $, base = 8 ft)
# Explanation:
## Step1: Use the parallelogram area formula
$ A = b \times h $, so $ h = \frac{A}{b} $ (where $ h = x $, $ A = 120 $, $ b = 8 $).
## Step2: Substitute the values
$ x = \frac{120}{8} $.
## Step3: Perform the division
$ \frac{120}{8} = 15 $.
# Answer:
The value of $ x $ is $ 15 \, \text{ft} $.

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QUESTION IMAGE

Question

Explanation:

Problem 1: Find the area of the square (8 m side)

Step1: Identify the formula for square area

Step2: Substitute the side length

Step3: Calculate the result

Step1: Recall the rectangle area formula

Step2: Substitute the values

Step3: Compute the product

Step1: Use the rectangle area formula

Step2: Substitute the values

Step3: Perform the division

Answer:

Problem 2: Find the area of the rectangle (7 in by 12 in)