To solve the problem of finding the area of each triangle, we will use the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Let's go through each triangle step by step.
Triangle 1:
- Base = 2 cm
- Height = 7 cm
\[
\text{Area} = \frac{1}{2} \times 2 \times 7 = \frac{1}{2} \times 14 = 7 \, \text{cm}^2
\]
Triangle 2:
- Base = 2 cm
- Height = 5 cm (since the height is perpendicular to the base)
\[
\text{Area} = \frac{1}{2} \times 2 \times 5 = \frac{1}{2} \times 10 = 5 \, \text{cm}^2
\]
Triangle 3:
- Base = 10 cm (sum of 7 cm and 3 cm)
- Height = 12 cm
\[
\text{Area} = \frac{1}{2} \times 10 \times 12 = \frac{1}{2} \times 120 = 60 \, \text{cm}^2
\]
Triangle 4:
- Base = 6 cm
- Height = 8 cm
\[
\text{Area} = \frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times 48 = 24 \, \text{cm}^2
\]
Triangle 5:
- This is an equilateral triangle with all sides equal to 5 cm.
- To find the height, we can use the Pythagorean theorem in one of the right triangles formed by dropping a perpendicular from one vertex to the opposite side:
- Half of the base = \( \frac{5}{2} = 2.5 \) cm
- Height \( h \) can be found using:
\[
h = \sqrt{5^2 - 2.5^2} = \sqrt{25 - 6.25} = \sqrt{18.75} = \frac{5\sqrt{3}}{2}
\]
- Now, calculate the area:
\[
\text{Area} = \frac{1}{2} \times 5 \times \frac{5\sqrt{3}}{2} = \frac{25\sqrt{3}}{4} \approx 10.83 \, \text{cm}^2
\]
Triangle 6:
- Base = 10 cm
- Height = 3 cm
\[
\text{Area} = \frac{1}{2} \times 10 \times 3 = \frac{1}{2} \times 30 = 15 \, \text{cm}^2
\]
Triangle 7:
- Base = 2 cm
- Height = 6 cm
\[
\text{Area} = \frac{1}{2} \times 2 \times 6 = \frac{1}{2} \times 12 = 6 \, \text{cm}^2
\]
Triangle 8:
- Base = 10 cm
- Height = 6 cm
\[
\text{Area} = \frac{1}{2} \times 10 \times 6 = \frac{1}{2} \times 60 = 30 \, \text{cm}^2
\]
Triangle 9:
- Base = 8 cm
- Height = 2 cm
\[
\text{Area} = \frac{1}{2} \times 8 \times 2 = \frac{1}{2} \times 16 = 8 \, \text{cm}^2
\]
Final Answers:
\[
\boxed{
\begin{array}{ccc}
7 \, \text{cm}^2 & 5 \, \text{cm}^2 & 60 \, \text{cm}^2 \\
24 \, \text{cm}^2 & 10.83 \, \text{cm}^2 & 15 \, \text{cm}^2 \\
6 \, \text{cm}^2 & 30 \, \text{cm}^2 & 8 \, \text{cm}^2
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of finding the area of a triangle worksheet.
