To find the area of the given figure, which consists of a rectangle and a triangle, we can calculate the area of each shape separately and then sum them up.
Step 1: Calculate the area of the rectangle.
The dimensions of the rectangle are:
- Width (base): 8 cm (the top of the rectangle)
- Height: 4 cm (the left side of the rectangle)
The area \( A_{rectangle} \) is given by the formula: \[ A_{rectangle} = \text{width} \times \text{height} = 8 , \text{cm} \times 4 , \text{cm} = 32 , \text{cm}^2 \]
Step 2: Calculate the area of the triangle.
The triangle is formed on the right side of the rectangle.
To calculate the area of the triangle, we need to know its base and height.
- Base of the triangle: The width of the rectangle, which is 8 cm.
- Height of the triangle: The remaining vertical side from the bottom to the top of the triangle (not provided), but we can deduce it based on the dimensions given.
Since the width of the base (entire bottom of the figure) is 10 cm and the width of the rectangle is 8 cm:
- The base of the triangle = 10 cm - 8 cm = 2 cm.
Now we need to determine the height of the triangle. The total height of the rectangle is 4 cm, and the top extends diagonally to form the triangle:
- The height of the triangle can be assumed to be the same as the left side which is 4 cm if we consider it extending to the top.
Now we calculate the area of the triangle \( A_{triangle} \) using the formula: \[ A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 , \text{cm} \times 4 , \text{cm} = \frac{1}{2} \times 8 , \text{cm}^2 = 4 , \text{cm}^2 \]
Step 3: Calculate the total area of the figure.
Now we can sum the areas of the rectangle and the triangle: \[ \text{Total Area} = A_{rectangle} + A_{triangle} = 32 , \text{cm}^2 + 4 , \text{cm}^2 = 36 , \text{cm}^2 \]
Thus, the area of the figure is \( \text{Total Area} = 36 , \text{cm}^2 \).
The final answer is: \[ \boxed{36} , \text{cm}^2 \]
5 answers