Here are the step-by-step solutions for each polygon.
To solve these, we use two main formulas:
1.
Perimeter = (Number of sides) $\times$ (Length of one side)
2.
Area = $\frac{1}{2} \times$ (Perimeter) $\times$ (Apothem/Height from center)
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1. Blue Pentagon (Top Left)
*
Shape: Regular Pentagon (5 sides)
*
Side length: 18 units
*
Apothem (height): 15 units
Step 1: Find Perimeter
$$5 \text{ sides} \times 18 = 90 \text{ units}$$
Step 2: Find Area
$$\text{Area} = \frac{1}{2} \times 90 \times 15$$
$$\text{Area} = 45 \times 15 = 675 \text{ square units}$$
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2. White Octagon (Top Right)
*
Shape: Regular Octagon (8 sides)
*
Side length: 10 m
*
Apothem (height): 12.1 m
Step 1: Find Perimeter
$$8 \text{ sides} \times 10 = 80 \text{ m}$$
Step 2: Find Area
$$\text{Area} = \frac{1}{2} \times 80 \times 12.1$$
$$\text{Area} = 40 \times 12.1 = 484 \text{ m}^2$$
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3. Grey Octagon (Middle Left)
*
Shape: Regular Octagon (8 sides)
*
Side length: 5 cm
*
Apothem ($a$): 6 cm
Step 1: Find Perimeter
$$8 \text{ sides} \times 5 = 40 \text{ cm}$$
Step 2: Find Area
$$\text{Area} = \frac{1}{2} \times 40 \times 6$$
$$\text{Area} = 20 \times 6 = 120 \text{ cm}^2$$
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4. Grey Hexagon (Middle Right)
*
Shape: Regular Hexagon (6 sides)
*
Side length: 5 cm
*
Apothem ($a$): 4.3 cm
Step 1: Find Perimeter
$$6 \text{ sides} \times 5 = 30 \text{ cm}$$
Step 2: Find Area
$$\text{Area} = \frac{1}{2} \times 30 \times 4.3$$
$$\text{Area} = 15 \times 4.3 = 64.5 \text{ cm}^2$$
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5. Grey Pentagon (Bottom Left)
*
Shape: Regular Pentagon (5 sides)
*
Side length: 10 cm
*
Apothem ($a$): 6.9 cm
Step 1: Find Perimeter
$$5 \text{ sides} \times 10 = 50 \text{ cm}$$
Step 2: Find Area
$$\text{Area} = \frac{1}{2} \times 50 \times 6.9$$
$$\text{Area} = 25 \times 6.9 = 172.5 \text{ cm}^2$$
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6. Grey Pentagon (Bottom Right)
*
Shape: Regular Pentagon (5 sides)
*
Side length: 2 cm
*
Apothem ($a$): 1.4 cm
Step 1: Find Perimeter
$$5 \text{ sides} \times 2 = 10 \text{ cm}$$
Step 2: Find Area
$$\text{Area} = \frac{1}{2} \times 10 \times 1.4$$
$$\text{Area} = 5 \times 1.4 = 7 \text{ cm}^2$$
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Final Answer:
1. Blue Pentagon:
* Perimeter:
90 units
* Area:
675 square units
2. White Octagon:
* Perimeter:
80 m
* Area:
484 m²
3. Grey Octagon:
* Perimeter:
40 cm
* Area:
120 cm²
4. Grey Hexagon:
* Perimeter:
30 cm
* Area:
64.5 cm²
5. Grey Pentagon (Large):
* Perimeter:
50 cm
* Area:
172.5 cm²
6. Grey Pentagon (Small):
* Perimeter:
10 cm
* Area:
7 cm²
Parent Tip: Review the logic above to help your child master the concept of area and perimeter of polygons worksheet pdf.
