A house-shaped figure where the base is a rectangle with a width of 10 cm and a height of 8 cm. A triangle sits on top of the rectangle with a base of 10 cm and a height of 6 cm. Question: What is the total area of the combined shape?

To find the total area of the combined house-shaped figure, we need to calculate the area of the rectangle and the area of the triangle separately, then add them together.

### 1. Area of the Rectangle:
The area \(A_{\text{rect}}\) of the rectangle is given by the formula:
\[
A_{\text{rect}} = \text{width} \times \text{height}
\]
Substituting the given values:
\[
A_{\text{rect}} = 10 \, \text{cm} \times 8 \, \text{cm} = 80 \, \text{cm}^2
\]

### 2. Area of the Triangle:
The area \(A_{\text{tri}}\) of the triangle is given by the formula:
\[
A_{\text{tri}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Substituting the given values:
\[
A_{\text{tri}} = \frac{1}{2} \times 10 \, \text{cm} \times 6 \, \text{cm} = \frac{1}{2} \times 60 \, \text{cm}^2 = 30 \, \text{cm}^2
\]

### 3. Total Area of the Combined Shape:
The total area \(A_{\text{total}}\) is the sum of the areas of the rectangle and the triangle:
\[
A_{\text{total}} = A_{\text{rect}} + A_{\text{tri}} = 80 \, \text{cm}^2 + 30 \, \text{cm}^2 = 110 \, \text{cm}^2
\]

**The total area of the combined shape is 110 square centimeters.**

Would you like more details or have any questions?

Here are some related questions to consider:
1. How would the total area change if the triangle's height were increased by 2 cm?
2. What is the perimeter of the combined house-shaped figure?
3. If the base of the triangle were reduced by half, how would that affect the total area?
4. How do you calculate the area of a complex shape made up of more than two simple shapes?
5. What is the area of the house-shaped figure if the dimensions are doubled?

**Tip:** Always remember that the area of a shape is a measure of the space inside it, so when calculating the area of a complex figure, break it down into simpler shapes.

Find the total area of a house-shaped figure composed of a rectangle with dimensions 10 cm by 8 cm and a triangle with a base of 10 cm and a height of 6 cm. This problem covers essential geometric concepts and is suitable for students in Grades 5-7.

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