To solve for the area of each triangle, we use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Let’s calculate the area for each triangle one by one.

a)

• Base = 6 cm
• Height = 5 cm $\text{Area} = \frac{1}{2} \times 6 \times 5 = 15 \, \text{cm}^2$

b)

• Base = 10 cm
• Height = 7 cm $\text{Area} = \frac{1}{2} \times 10 \times 7 = 35 \, \text{cm}^2$

c)

• Base = 6 cm
• Height = 5 cm $\text{Area} = \frac{1}{2} \times 6 \times 5 = 15 \, \text{cm}^2$

d)

• Base = 10 cm
• Height = 7 cm $\text{Area} = \frac{1}{2} \times 10 \times 7 = 35 \, \text{cm}^2$

e)

• Base = 7 cm
• Height = 10 cm $\text{Area} = \frac{1}{2} \times 7 \times 10 = 35 \, \text{cm}^2$

Thus, the areas of the triangles are:

• a) 15 cm²
• b) 35 cm²
• c) 15 cm²
• d) 35 cm²
• e) 35 cm²

Do you need more details or have any other questions?

Here are 5 related questions for practice:

1. What would be the area of a triangle with a base of 8 cm and height of 5 cm?
2. How does the area formula change for equilateral triangles?
3. Can you calculate the area of a triangle using only the side lengths?
4. What is Heron's formula for triangle area?
5. How would the area change if the base is doubled but the height stays the same?

Tip: In right-angled triangles, the legs can always be considered as the base and height!