Let's break this problem down step by step.

Given:

• The outer shape is a rectangle.
• The dimensions of the rectangle are 8 cm in height and an unknown width (assumed to be same as height, 8 cm).
• A triangular section is removed from the bottom, with a height of 4 cm and a base equal to the width of the rectangle (8 cm).

Step 1: Calculate the Area of the Rectangle

$A_{\text{rectangle}} = \text{width} \times \text{height} = 8 \times 8 = 64 \text{ cm}^2$

Step 2: Calculate the Area of the Triangle

The area of a triangle is given by: $A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}$ Substituting values: $A_{\text{triangle}} = \frac{1}{2} \times 8 \times 4 = \frac{32}{2} = 16 \text{ cm}^2$

Step 3: Calculate the Shaded Area

$A_{\text{shaded}} = A_{\text{rectangle}} - A_{\text{triangle}}$ $A_{\text{shaded}} = 64 - 16 = 48 \text{ cm}^2$

Final Answer:

The shaded area is 48 cm².

Would you like a more detailed explanation or any variations on this problem?

Related Questions:

1. How would the shaded area change if the triangle's height was 6 cm instead of 4 cm?
2. What is the perimeter of the shaded region?
3. How can we generalize this method for different rectangle and triangle sizes?
4. If the rectangle was a square with side x, how would the shaded area be expressed in terms of x?
5. How can this problem be solved using algebraic expressions?

Tip:

Always double-check whether the removed shape is completely inside the larger shape to ensure correct subtraction of areas.