The shape in the image is a right-angled triangle, and the goal is to find its area.

The formula for the area $A$ of a right-angled triangle is: $A = \frac{1}{2} \times \text{base} \times \text{height}$

Step 1: Identify the base and height

From the diagram:

• The base of the triangle is $7 \, \text{cm}$.
• The height of the triangle is $8 \, \text{cm}$.

Step 2: Substitute the values

Substitute these values into the area formula: $A = \frac{1}{2} \times 7 \, \text{cm} \times 8 \, \text{cm}$

Step 3: Calculate the area

$A = \frac{1}{2} \times 56 = 28 \, \text{cm}^2$

Final Answer

The area of the triangle is: $\boxed{28 \, \text{cm}^2}$

Would you like further explanation on this?

Here are some additional questions to deepen your understanding:

1. How would the area change if the base was doubled?
2. What is the perimeter of this triangle?
3. How can you find the length of the hypotenuse using the Pythagorean theorem?
4. If the height was halved, what would be the new area?
5. What is the relationship between the area of a triangle and a rectangle with the same base and height?

Tip: For any right-angled triangle, the hypotenuse can always be found using the Pythagorean theorem, which is useful for verifying triangle properties.