To solve the problem, we need to calculate the
area of each triangle shown in the image. The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Let's go through each triangle step by step.
---
Triangle 1:
- Base = 2 cm
- Height = 3 cm
\[
\text{Area} = \frac{1}{2} \times 2 \times 3 = \frac{1}{2} \times 6 = 3 \, \text{cm}^2
\]
---
Triangle 2:
This is an
equilateral triangle with all sides equal to 4 cm. For an equilateral triangle, the height can be calculated using the formula:
\[
\text{Height} = \frac{\sqrt{3}}{2} \times \text{side}
\]
Here, the side length is 4 cm:
\[
\text{Height} = \frac{\sqrt{3}}{2} \times 4 = 2\sqrt{3} \, \text{cm}
\]
Now, use the area formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 2\sqrt{3} = 4\sqrt{3} \, \text{cm}^2
\]
---
Triangle 3:
- Base = 1 cm
- Height = 6 cm
\[
\text{Area} = \frac{1}{2} \times 1 \times 6 = \frac{1}{2} \times 6 = 3 \, \text{cm}^2
\]
---
Triangle 4:
- Base = 5 cm
- Height = 2 cm
\[
\text{Area} = \frac{1}{2} \times 5 \times 2 = \frac{1}{2} \times 10 = 5 \, \text{cm}^2
\]
---
Triangle 5:
This is a
right triangle with the base and height given directly:
- Base = 4 cm
- Height = 2 cm
\[
\text{Area} = \frac{1}{2} \times 4 \times 2 = \frac{1}{2} \times 8 = 4 \, \text{cm}^2
\]
---
Triangle 6:
- Base = 3 cm
- Height = 8 cm
\[
\text{Area} = \frac{1}{2} \times 3 \times 8 = \frac{1}{2} \times 24 = 12 \, \text{cm}^2
\]
---
Final Answers:
\[
\boxed{
\begin{aligned}
1) & \, 3 \, \text{cm}^2 \\
2) & \, 4\sqrt{3} \, \text{cm}^2 \\
3) & \, 3 \, \text{cm}^2 \\
4) & \, 5 \, \text{cm}^2 \\
5) & \, 4 \, \text{cm}^2 \\
6) & \, 12 \, \text{cm}^2
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of is it a right triangle worksheet.
