Problem: Calculate the area of each rhombus using the appropriate formula.
####
Formulas to Use:
1.
Using diagonals: \( A = \frac{d_1 \cdot d_2}{2} \)
2.
Using base and height: \( A = b \cdot h \)
####
Step-by-Step Solution:
---
Rhombus 1:
-
Given: Diagonals \( d_1 = 15 \, \text{cm} \) and \( d_2 = 10 \, \text{cm} \).
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Formula: \( A = \frac{d_1 \cdot d_2}{2} \)
-
Calculation:
\[
A = \frac{15 \cdot 10}{2} = \frac{150}{2} = 75 \, \text{cm}^2
\]
-
Answer: \( 75 \, \text{cm}^2 \)
---
Rhombus 2:
-
Given: Base \( b = 13 \, \text{cm} \) and height \( h = 12 \, \text{cm} \).
-
Formula: \( A = b \cdot h \)
-
Calculation:
\[
A = 13 \cdot 12 = 156 \, \text{cm}^2
\]
-
Answer: \( 156 \, \text{cm}^2 \)
---
Rhombus 3:
-
Given: Diagonals \( d_1 = 6 \, \text{cm} \) (since \( 3 + 3 = 6 \)) and \( d_2 = 10 \, \text{cm} \).
-
Formula: \( A = \frac{d_1 \cdot d_2}{2} \)
-
Calculation:
\[
A = \frac{6 \cdot 10}{2} = \frac{60}{2} = 30 \, \text{cm}^2
\]
-
Answer: \( 30 \, \text{cm}^2 \)
---
Rhombus 4:
-
Given: Base \( b = 8 \, \text{cm} \) and height \( h = 7 \, \text{cm} \).
-
Formula: \( A = b \cdot h \)
-
Calculation:
\[
A = 8 \cdot 7 = 56 \, \text{cm}^2
\]
-
Answer: \( 56 \, \text{cm}^2 \)
---
Rhombus 5:
-
Given: Diagonals \( d_1 = 22 \, \text{cm} \) and \( d_2 = 24 \, \text{cm} \).
-
Formula: \( A = \frac{d_1 \cdot d_2}{2} \)
-
Calculation:
\[
A = \frac{22 \cdot 24}{2} = \frac{528}{2} = 264 \, \text{cm}^2
\]
-
Answer: \( 264 \, \text{cm}^2 \)
---
Rhombus 6:
-
Given: Base \( b = 9 \, \text{cm} \) and height \( h = 4 \, \text{cm} \).
-
Formula: \( A = b \cdot h \)
-
Calculation:
\[
A = 9 \cdot 4 = 36 \, \text{cm}^2
\]
-
Answer: \( 36 \, \text{cm}^2 \)
---
Final Answers:
\[
\boxed{
\begin{array}{ccc}
1) & 75 \, \text{cm}^2 & \\
2) & 156 \, \text{cm}^2 & \\
3) & 30 \, \text{cm}^2 & \\
4) & 56 \, \text{cm}^2 & \\
5) & 264 \, \text{cm}^2 & \\
6) & 36 \, \text{cm}^2 & \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of area of rhombus worksheet.
