Area And Perimeter Of Shapes Worksheets Pdf - Worksheets Joy D15 - Free Printable

To solve the problem of finding the areas of the given polygons, we will use the appropriate formulas for each shape. Let's go through each part step by step.

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1. Squares

The formula for the area of a square is:
\[ \text{Area} = \text{side}^2 \]

#### Problem 1:
Side = 21 cm
\[ \text{Area} = 21^2 = 441 \, \text{cm}^2 \]

#### Problem 2:
Side = 16 ft
\[ \text{Area} = 16^2 = 256 \, \text{ft}^2 \]

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2. Rectangles

The formula for the area of a rectangle is:
\[ \text{Area} = \text{length} \times \text{width} \]

#### Problem 3:
Length = 11 cm, Width = 8 cm
\[ \text{Area} = 11 \times 8 = 88 \, \text{cm}^2 \]

#### Problem 4:
Length = 14 in, Width = 12 in
\[ \text{Area} = 14 \times 12 = 168 \, \text{in}^2 \]

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3. Parallelograms

The formula for the area of a parallelogram is:
\[ \text{Area} = \text{base} \times \text{height} \]

#### Problem 5:
Base = 21 yd, Height = 18 yd
\[ \text{Area} = 21 \times 18 = 378 \, \text{yd}^2 \]

#### Problem 6:
Base = 23 cm, Height = 4 cm
\[ \text{Area} = 23 \times 4 = 92 \, \text{cm}^2 \]

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4. Rhombuses

The formula for the area of a rhombus is:
\[ \text{Area} = \frac{\text{diagonal}_1 \times \text{diagonal}_2}{2} \]

#### Problem 7:
Diagonal 1 = 8 cm, Diagonal 2 = 8.5 cm
\[ \text{Area} = \frac{8 \times 8.5}{2} = \frac{68}{2} = 34 \, \text{cm}^2 \]

#### Problem 8:
Diagonal 1 = 7 in, Diagonal 2 = 7.5 in
\[ \text{Area} = \frac{7 \times 7.5}{2} = \frac{52.5}{2} = 26.25 \, \text{in}^2 \]

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5. Triangles

The formula for the area of a triangle is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

#### Problem 9:
Base = 10.5 ft, Height = 11.5 ft
\[ \text{Area} = \frac{1}{2} \times 10.5 \times 11.5 = \frac{1}{2} \times 120.75 = 60.375 \, \text{ft}^2 \]

#### Problem 10:
Base = 6.5 cm, Height = 7.5 cm
\[ \text{Area} = \frac{1}{2} \times 6.5 \times 7.5 = \frac{1}{2} \times 48.75 = 24.375 \, \text{cm}^2 \]

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6. Trapezoids

The formula for the area of a trapezoid is:
\[ \text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} \]

#### Problem 11:
Base 1 = 10 in, Base 2 = 14 in, Height = 6 in
\[ \text{Area} = \frac{1}{2} \times (10 + 14) \times 6 = \frac{1}{2} \times 24 \times 6 = \frac{1}{2} \times 144 = 72 \, \text{in}^2 \]

#### Problem 12:
Base 1 = 10 in, Base 2 = 5 in, Height = 10 in
\[ \text{Area} = \frac{1}{2} \times (10 + 5) \times 10 = \frac{1}{2} \times 15 \times 10 = \frac{1}{2} \times 150 = 75 \, \text{in}^2 \]

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Final Answers

1. \( 441 \, \text{cm}^2 \)
2. \( 256 \, \text{ft}^2 \)
3. \( 88 \, \text{cm}^2 \)
4. \( 168 \, \text{in}^2 \)
5. \( 378 \, \text{yd}^2 \)
6. \( 92 \, \text{cm}^2 \)
7. \( 34 \, \text{cm}^2 \)
8. \( 26.25 \, \text{in}^2 \)
9. \( 60.375 \, \text{ft}^2 \)
10. \( 24.375 \, \text{cm}^2 \)
11. \( 72 \, \text{in}^2 \)
12. \( 75 \, \text{in}^2 \)

\[
\boxed{
\begin{array}{ll}
1. & 441 \, \text{cm}^2 \\
2. & 256 \, \text{ft}^2 \\
3. & 88 \, \text{cm}^2 \\
4. & 168 \, \text{in}^2 \\
5. & 378 \, \text{yd}^2 \\
6. & 92 \, \text{cm}^2 \\
7. & 34 \, \text{cm}^2 \\
8. & 26.25 \, \text{in}^2 \\
9. & 60.375 \, \text{ft}^2 \\
10. & 24.375 \, \text{cm}^2 \\
11. & 72 \, \text{in}^2 \\
12. & 75 \, \text{in}^2 \\
\end{array}
}
\]