To find the area of the triangles in the provided image, we can use the formula for the area of a triangle, which is $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$. Let's solve each problem step by step.

Problem (e)

• Base (b): 26 m
• Height (h): 15 m (perpendicular distance)

$\text{Area} = \frac{1}{2} \times 26 \times 15$ $\text{Area} = \frac{1}{2} \times 390$ $\text{Area} = 195 \text{ m}^2$

Problem (f)

• Base (b): 5 cm
• Height (h): 6 cm

$\text{Area} = \frac{1}{2} \times 5 \times 6$ $\text{Area} = \frac{1}{2} \times 30$ $\text{Area} = 15 \text{ cm}^2$

Problem (g)

• Base (b): 42 m
• Height (h): 45 m

$\text{Area} = \frac{1}{2} \times 42 \times 45$ $\text{Area} = \frac{1}{2} \times 1890$ $\text{Area} = 945 \text{ m}^2$

Problem (h)

• Base (b): 20 cm
• Height (h): 15 cm (perpendicular height)

$\text{Area} = \frac{1}{2} \times 20 \times 15$ $\text{Area} = \frac{1}{2} \times 300$ $\text{Area} = 150 \text{ cm}^2$

Would you like details on any specific step or have any other questions? Here are some related questions to further your understanding:

1. How do you determine the base and height of a triangle in non-right triangles?
2. Can the formula for the area of a triangle be used for all types of triangles?
3. What other methods can be used to find the area of a triangle if the base and height are not given?
4. How does the Pythagorean theorem help in finding the area of right-angled triangles?
5. How would you find the area of a triangle if you only know the lengths of all three sides?

Tip: When working with triangles, always ensure that the height is perpendicular to the base to correctly apply the area formula.