Area of Quadrilaterals worksheet for calculating areas of squares, rectangles, parallelograms, and rhombuses.

Here are the solutions for the area problems on the worksheet.

Section A: Squares and Rectangles

*Formula: Area = Length × Width (or Side × Side)*

1) $10 \text{ cm} \times 10 \text{ cm} = 100 \text{ cm}^2$
2) $6 \text{ cm} \times 6 \text{ cm} = 36 \text{ cm}^2$
3) $12 \text{ cm} \times 12 \text{ cm} = 144 \text{ cm}^2$
4) $9 \text{ mm} \times 9 \text{ mm} = 81 \text{ mm}^2$
5) $9 \text{ cm} \times 4 \text{ cm} = 36 \text{ cm}^2$
6) $11 \text{ cm} \times 3 \text{ cm} = 33 \text{ cm}^2$
7) $20 \text{ cm} \times 3 \text{ cm} = 60 \text{ cm}^2$
8) $8 \text{ cm} \times 4 \text{ cm} = 32 \text{ cm}^2$

Section B: Parallelograms and Rhombuses

*Formulas:*
* *Parallelogram/Rhombus Area = Base × Height*
* *Rhombus (using diagonals) Area = $\frac{\text{Diagonal}_1 \times \text{Diagonal}_2}{2}$*

1) Base is $9$, height is $6$.
$9 \times 6 = 54 \text{ cm}^2$

2) Base is $22$, height is $12$.
$22 \times 12 = 264 \text{ cm}^2$

3) Base is $4$, height is $5$. (Ignore the slanted side length of $5.5$).
$4 \times 5 = 20 \text{ cm}^2$

4) Base is $5$, height is $7$. (Ignore the slanted side length of $8$).
$5 \times 7 = 35 \text{ cm}^2$

5) Diagonals are $14$ and $20$.
$(14 \times 20) / 2 = 280 / 2 = 140 \text{ cm}^2$

6) This shape is made of two triangles with a shared base of $10$ and heights of $8$ each. Or, treat it as a rhombus with diagonals $16$ ($8+8$) and $10$.
$(16 \times 10) / 2 = 160 / 2 = 80 \text{ cm}^2$

Final Answer:
Section A
1) 100 cm²
2) 36 cm²
3) 144 cm²
4) 81 mm²
5) 36 cm²
6) 33 cm²
7) 60 cm²
8) 32 cm²

Section B
1) 54 cm²
2) 264 cm²
3) 20 cm²
4) 35 cm²
5) 140 cm²
6) 80 cm²