Question

1-22 find the perimeter and area of each figure below. homework help a) figure of a composite square - shaped figure b) figure of a parallelogram with base 7 ft, side 5 ft, height 4 ft answer: a. b. c.

Explanation:

Part a) (Assuming each square has side length \( s = 1 \) unit, since no unit is given)

Perimeter:

Step 1: Count outer sides

Each square has 4 sides, but shared sides are not part of the perimeter. Let's count the number of outer - facing sides. By carefully examining the cross - shaped figure:

• Horizontally: The top and bottom parts and the middle horizontal part. After counting, we find that the total number of outer - facing sides is 16 (by counting each exposed side of the squares). Since each side is length 1, the perimeter \( P=16\times1 = 16\) units.

Step 2: Calculate Area

The area of a square is \( A_{square}=s^{2}\). Here, \( s = 1 \), so the area of one square is \( 1\times1 = 1\) square unit. Count the number of squares: There are 9 squares. So the area \( A = 9\times1=9\) square units.

Part b) (For the parallelogram with base \( b = 7\) ft, side \( l = 5\) ft, and height \( h = 4\) ft)

Perimeter:

Step 1: Recall the formula for the perimeter of a parallelogram

The perimeter of a parallelogram is given by \( P = 2(b + l)\), where \( b \) is the base and \( l \) is the length of the side.
Substitute \( b = 7\) ft and \( l = 5\) ft into the formula: \( P=2(7 + 5)\)

Step 2: Simplify the perimeter formula

\( P=2\times12=24\) ft.

Area:

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

The area of a parallelogram is given by \( A=b\times h\), where \( b \) is the base and \( h \) is the height.
Substitute \( b = 7\) ft and \( h = 4\) ft into the formula: \( A = 7\times4\)

Step 2: Calculate the area

\( A = 28\) square feet.

Answer:

s:

a)

• Perimeter: \( \boldsymbol{16}\) units (assuming side length of square is 1 unit)
• Area: \( \boldsymbol{9}\) square units (assuming side length of square is 1 unit)

b)

• Perimeter: \( \boldsymbol{24}\) ft
• Area: \( \boldsymbol{28}\) square feet