Here are the step-by-step solutions for each problem on the worksheet.
1. Triangle
*
Perimeter: Add all three sides together.
$8.6 + 8.6 + 10.8 = 28$ m
*
Area: Use the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
$\text{Area} = 0.5 \times 10.8 \times 5.4$
$\text{Area} = 29.16$ m²
2. Square
*
Perimeter: A square has 4 equal sides. Multiply one side by 4.
$26.1 \times 4 = 104.4$ m
*
Area: Multiply side by side (square the side).
$26.1 \times 26.1 = 681.21$ m²
3. Rectangle
*
Perimeter: Add all four sides ($2 \times \text{length} + 2 \times \text{width}$).
$(2 \times 8.1) + (2 \times 4.2)$
$16.2 + 8.4 = 24.6$ cm
*
Area: Multiply length by width.
$8.1 \times 4.2 = 34.02$ cm²
4. Rhombus (Diamond)
*
Perimeter: Add all four sides together.
$5.3 + 5.3 + 5.3 + 5.3 = 21.2$ ft
*(Note: The label "13.3 ft" appears to be a typo in the diagram because the other sides are labeled 5.3 ft. We use the consistent value of 5.3 ft).*
*
Area: This shape is made of two identical triangles.
Area of one triangle = $\frac{1}{2} \times \text{base} \times \text{height}$
Base = 8 ft, Height = 3 ft.
Area of one triangle = $0.5 \times 8 \times 3 = 12$ sq ft.
Total Area = $12 \times 2 = 24$ ft²
5. Pentagon
*
Perimeter: A regular pentagon has 5 equal sides.
$6.8 \times 5 = 34$ cm
*
Area: Use the formula $\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{apothem}$ (the height line inside).
$\text{Area} = 0.5 \times 34 \times 4.8$
$\text{Area} = 17 \times 4.8 = 81.6$ cm²
6. Hexagon
*
Perimeter: A regular hexagon has 6 equal sides.
$7.7 \times 6 = 46.2$ m
*
Area: Use the formula $\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{apothem}$.
$\text{Area} = 0.5 \times 46.2 \times 6.1$
$\text{Area} = 23.1 \times 6.1 = 140.91$ m²
7. Nonagon (9-sided polygon)
*
Perimeter: It has 9 equal sides.
$9.9 \times 9 = 89.1$ ft
*
Area: Use the formula $\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{radius/apothem}$.
$\text{Area} = 0.5 \times 89.1 \times 7.9$
$\text{Area} = 44.55 \times 7.9 = 351.945$ ft²
8. Trapezoid
*
Perimeter: Add all four outer sides together.
$18.7 + 12.8 + 24.3 + 10.1 = 65.9$ mm
*
Area: Use the formula $\text{Area} = \frac{\text{top} + \text{bottom}}{2} \times \text{height}$.
Top = 18.7, Bottom = 24.3, Height = 10.1 (the straight vertical side).
$\text{Average width} = \frac{18.7 + 24.3}{2} = \frac{43}{2} = 21.5$
$\text{Area} = 21.5 \times 10.1 = 217.15$ mm²
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Final Answer:
1. Area =
29.16 m², Perimeter =
28 m
2. Area =
681.21 m², Perimeter =
104.4 m
3. Area =
34.02 cm², Perimeter =
24.6 cm
4. Area =
24 ft², Perimeter =
21.2 ft
5. Area =
81.6 cm², Perimeter =
34 cm
6. Area =
140.91 m², Perimeter =
46.2 m
7. Area =
351.945 ft², Perimeter =
89.1 ft
8. Area =
217.15 mm², Perimeter =
65.9 mm
Parent Tip: Review the logic above to help your child master the concept of finding area of polygons worksheet.
