Problem Analysis:
The given shape is a combination of a rectangle and a right triangle. The task is to calculate the
area of this combined shape. Let's break it down step by step.
#### Step 1: Identify the components of the shape
- The shape consists of:
1. A
rectangle with dimensions \(6 \, \text{cm} \times 5 \, \text{cm}\).
2. A
right triangle attached to the rectangle. The base of the triangle is the difference between the total length of the bottom side (14 cm) and the width of the rectangle (6 cm). The height of the triangle is the same as the height of the rectangle (5 cm).
#### Step 2: Calculate the area of the rectangle
The formula for the area of a rectangle is:
\[
\text{Area of rectangle} = \text{length} \times \text{width}
\]
Here, the length is \(6 \, \text{cm}\) and the width is \(5 \, \text{cm}\):
\[
\text{Area of rectangle} = 6 \times 5 = 30 \, \text{cm}^2
\]
#### Step 3: Calculate the area of the right triangle
The formula for the area of a triangle is:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
- The base of the triangle is the difference between the total length of the bottom side (14 cm) and the width of the rectangle (6 cm):
\[
\text{Base of triangle} = 14 - 6 = 8 \, \text{cm}
\]
- The height of the triangle is the same as the height of the rectangle, which is \(5 \, \text{cm}\).
Now, calculate the area of the triangle:
\[
\text{Area of triangle} = \frac{1}{2} \times 8 \times 5 = \frac{1}{2} \times 40 = 20 \, \text{cm}^2
\]
#### Step 4: Calculate the total area of the combined shape
The total area is the sum of the area of the rectangle and the area of the triangle:
\[
\text{Total area} = \text{Area of rectangle} + \text{Area of triangle}
\]
\[
\text{Total area} = 30 + 20 = 50 \, \text{cm}^2
\]
Final Answer:
\[
\boxed{50}
\]
Parent Tip: Review the logic above to help your child master the concept of composite figure.
