To calculate the area of a compound shape consisting of a square and a triangle, we need to find the areas of both individual shapes and sum them together.

Understanding Compound Shapes

A compound shape is formed by combining two or more simple geometric figures. In this example, we will work with a square and a triangle. To determine the total area of the compound shape, we will first compute the area of each shape separately.

Area of the Square

The area of a square is calculated using the formula:

If we denote the side length of the square as $s$, then the area can be expressed as:

Area of the Triangle

The area of a triangle is determined using the formula:

For a triangle with a base $b$ and a height $h$, the area can be calculated as:

Calculating the Total Area

After calculating the areas of both shapes, we can find the total area of the compound shape by adding them together:

Example Calculation

Let’s illustrate this with an example. Suppose the side length of the square is $4 \, \text{cm}$, the base of the triangle is $4 \, \text{cm}$, and the height of the triangle is $3 \, \text{cm}$. We can compute the areas as follows:

1. Area of the square:

   $$\text{Area of square} = 4 \times 4 = 16 \, \text{cm}^2$$

2. Area of the triangle:

   $$\text{Area of triangle} = \frac{1}{2} \times 4 \times 3 = 6 \, \text{cm}^2$$

3. Total area of the compound shape:

   $$\text{Total area} = 16 \, \text{cm}^2 + 6 \, \text{cm}^2 = 22 \, \text{cm}^2$$

Conclusion

By summing the areas of the square and the triangle, we find that the total area of the compound shape is $22 \, \text{cm}^2$. This method of breaking down the problem into simpler components allows for a straightforward calculation of compound shapes.