To find the area of the shape, we can split it into two parts:

1. A rectangle (the bottom portion).
2. A triangle (the slanted portion at the top).

Step-by-step solution:

1. Find the area of the rectangle:

The rectangle's dimensions are:

• Height = $7 \, \text{cm}$,
• Base = $8 \, \text{cm}$.

The area of the rectangle is: $\text{Area of rectangle} = \text{base} \times \text{height} = 8 \times 7 = 56 \, \text{cm}^2.$

2. Find the area of the triangle:

The triangle has:

• Base = $8 \, \text{cm}$ (the same as the bottom of the rectangle),
• Height = $6 \, \text{cm}$ (perpendicular from the top to the base).

The area of a triangle is given by: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}.$

Substitute the values: $\text{Area of triangle} = \frac{1}{2} \times 8 \times 6 = 24 \, \text{cm}^2.$

3. Total area:

Add the areas of the rectangle and triangle: $\text{Total area} = 56 + 24 = 80 \, \text{cm}^2.$

Final Answer:

The total area of the shape is $80 \, \text{cm}^2$.

Would you like a deeper breakdown or visual explanation?

Related Questions:

1. How can we calculate the area of irregular shapes?
2. How do we determine the dimensions of a shape from a given area?
3. What other formulas exist for finding the area of polygons?
4. How does the height of the triangle affect the area calculation?
5. How would we approach this problem if one of the measurements was missing?

Tip:

Always break complex shapes into basic geometric parts for easier area calculations!