To solve the problem of finding the area of each rhombus, we use the formula for the area of a rhombus when the lengths of its diagonals are given:
\[
\text{Area} = \frac{1}{2} \times d_1 \times d_2
\]
where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.
Let's solve each problem step by step.
Problem 1:
- Diagonals: \( AC = 2 \, \text{yd} \), \( BD = 8 \, \text{yd} \)
- Area:
\[
\text{Area} = \frac{1}{2} \times 2 \times 8 = \frac{1}{2} \times 16 = 8 \, \text{yd}^2
\]
Problem 2:
- Diagonals: \( PR = 4 \, \text{in} \), \( QS = 6 \, \text{in} \)
- Area:
\[
\text{Area} = \frac{1}{2} \times 4 \times 6 = \frac{1}{2} \times 24 = 12 \, \text{in}^2
\]
Problem 3:
- Diagonals: \( EG = 12 \, \text{ft} \), \( FH = 5 \, \text{ft} \)
- Area:
\[
\text{Area} = \frac{1}{2} \times 12 \times 5 = \frac{1}{2} \times 60 = 30 \, \text{ft}^2
\]
Problem 4:
- Diagonals: \( XZ = 7 \, \text{in} \), \( WY = 3 \, \text{in} \)
- Area:
\[
\text{Area} = \frac{1}{2} \times 7 \times 3 = \frac{1}{2} \times 21 = 10.5 \, \text{in}^2
\]
Problem 5:
- Diagonals: \( LN = 17 \, \text{ft} \), \( KM = 10 \, \text{ft} \)
- Area:
\[
\text{Area} = \frac{1}{2} \times 17 \times 10 = \frac{1}{2} \times 170 = 85 \, \text{ft}^2
\]
Problem 6:
- Diagonals: \( TV = 16 \, \text{yd} \), \( SU = 9 \, \text{yd} \)
- Area:
\[
\text{Area} = \frac{1}{2} \times 16 \times 9 = \frac{1}{2} \times 144 = 72 \, \text{yd}^2
\]
Problem 7:
- Diagonals: \( UW = 11 \, \text{ft} \), \( TV = 13 \, \text{ft} \)
- Area:
\[
\text{Area} = \frac{1}{2} \times 11 \times 13 = \frac{1}{2} \times 143 = 71.5 \, \text{ft}^2
\]
Problem 8:
- Diagonals: \( DF = 18 \, \text{yd} \), \( CE = 8 \, \text{yd} \)
- Area:
\[
\text{Area} = \frac{1}{2} \times 18 \times 8 = \frac{1}{2} \times 144 = 72 \, \text{yd}^2
\]
Problem 9:
- Diagonals: \( QS = 17 \, \text{in} \), \( RT = 14 \, \text{in} \)
- Area:
\[
\text{Area} = \frac{1}{2} \times 17 \times 14 = \frac{1}{2} \times 238 = 119 \, \text{in}^2
\]
Final Answers:
\[
\boxed{
\begin{array}{ccc}
1) & 8 \, \text{yd}^2 & \\
2) & 12 \, \text{in}^2 & \\
3) & 30 \, \text{ft}^2 & \\
4) & 10.5 \, \text{in}^2 & \\
5) & 85 \, \text{ft}^2 & \\
6) & 72 \, \text{yd}^2 & \\
7) & 71.5 \, \text{ft}^2 & \\
8) & 72 \, \text{yd}^2 & \\
9) & 119 \, \text{in}^2 & \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of area of a rhombus worksheet.
