To solve the problem of finding the area of each triangle, we will use the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
We will apply this formula to each triangle in the image. Let's go through each one step by step.
---
1)
-
Base = 7 yd
-
Height = 5 yd
\[
\text{Area} = \frac{1}{2} \times 7 \times 5 = \frac{1}{2} \times 35 = 17.5 \, \text{yd}^2
\]
Answer: \( 17.5 \, \text{yd}^2 \)
---
2)
-
Base = 6 ft
-
Height = 8 ft
\[
\text{Area} = \frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times 48 = 24 \, \text{ft}^2
\]
Answer: \( 24 \, \text{ft}^2 \)
---
3)
-
Base = 12 in
-
Height = 15 in
\[
\text{Area} = \frac{1}{2} \times 12 \times 15 = \frac{1}{2} \times 180 = 90 \, \text{in}^2
\]
Answer: \( 90 \, \text{in}^2 \)
---
4)
-
Base = 11 ft
-
Height = 11 ft
\[
\text{Area} = \frac{1}{2} \times 11 \times 11 = \frac{1}{2} \times 121 = 60.5 \, \text{ft}^2
\]
Answer: \( 60.5 \, \text{ft}^2 \)
---
5)
-
Base = 10 in
-
Height = 5 in
\[
\text{Area} = \frac{1}{2} \times 10 \times 5 = \frac{1}{2} \times 50 = 25 \, \text{in}^2
\]
Answer: \( 25 \, \text{in}^2 \)
---
6)
-
Base = 13 yd
-
Height = 7 yd
\[
\text{Area} = \frac{1}{2} \times 13 \times 7 = \frac{1}{2} \times 91 = 45.5 \, \text{yd}^2
\]
Answer: \( 45.5 \, \text{yd}^2 \)
---
7)
-
Base = 19 in
-
Height = 14 in
\[
\text{Area} = \frac{1}{2} \times 19 \times 14 = \frac{1}{2} \times 266 = 133 \, \text{in}^2
\]
Answer: \( 133 \, \text{in}^2 \)
---
8)
-
Base = 8 yd
-
Height = 4 yd
\[
\text{Area} = \frac{1}{2} \times 8 \times 4 = \frac{1}{2} \times 32 = 16 \, \text{yd}^2
\]
Answer: \( 16 \, \text{yd}^2 \)
---
9)
-
Base = 18 ft
-
Height = 10 ft
\[
\text{Area} = \frac{1}{2} \times 18 \times 10 = \frac{1}{2} \times 180 = 90 \, \text{ft}^2
\]
Answer: \( 90 \, \text{ft}^2 \)
---
Final Answers:
\[
\boxed{
\begin{array}{lll}
1) & 17.5 \, \text{yd}^2 & \\
2) & 24 \, \text{ft}^2 & \\
3) & 90 \, \text{in}^2 & \\
4) & 60.5 \, \text{ft}^2 & \\
5) & 25 \, \text{in}^2 & \\
6) & 45.5 \, \text{yd}^2 & \\
7) & 133 \, \text{in}^2 & \\
8) & 16 \, \text{yd}^2 & \\
9) & 90 \, \text{ft}^2 & \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of triangles area worksheet.
