To calculate the area of the triangle in the image, we use the formula for the area of a triangle:

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

From the diagram:

• The base of the triangle is 15 cm.
• The height (perpendicular distance from the base) is 6 cm.

Substituting the values:

$\text{Area} = \frac{1}{2} \times 15 \, \text{cm} \times 6 \, \text{cm}$ $\text{Area} = \frac{1}{2} \times 90 \, \text{cm}^2 = 45 \, \text{cm}^2.$

Final Answer:

The area of the triangle is 45 cm².

Would you like more explanation or have any questions?

Here are 5 related questions you might explore:

1. How would the area change if the base were doubled but the height stayed the same?
2. What if the height were halved while the base stayed constant?
3. How would the formula change if we used the side lengths but no height was given?
4. Can you calculate the area of a triangle using trigonometry?
5. How does the formula for the area of a triangle differ from that for a rectangle?

Tip: Remember that the base and height must always be perpendicular to each other when applying the area formula for triangles.