https://file.aiquickdraw.com/mathbot/file/1727194477900rjjio0t8.jpg

The given diagram resembles a combination of geometric shapes: a triangle on top and a rectangle below. Let’s break down the shape and calculate its area step by step.

### Step 1: Split the Shape
The shape consists of:
1. **A triangle** at the top with:
   - Base = 6 cm (calculated by subtracting the side lengths of 4 cm each from the total top length of 12 cm).
   - Height = 4 cm.
   
2. **A rectangle** at the bottom:
   - Width = 6 cm.
   - Height = 10 cm.

### Step 2: Area of the Triangle
The formula for the area of a triangle is:

\[
\text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]

\[
\text{Area of Triangle} = \frac{1}{2} \times 6 \, \text{cm} \times 4 \, \text{cm} = 12 \, \text{cm}^2
\]

### Step 3: Area of the Rectangle
The formula for the area of a rectangle is:

\[
\text{Area of Rectangle} = \text{Width} \times \text{Height}
\]

\[
\text{Area of Rectangle} = 6 \, \text{cm} \times 10 \, \text{cm} = 60 \, \text{cm}^2
\]

### Step 4: Total Area
Now, sum the areas of the triangle and the rectangle:

\[
\text{Total Area} = 12 \, \text{cm}^2 + 60 \, \text{cm}^2 = 72 \, \text{cm}^2
\]

### Conclusion:
The total area of the shape is **72 cm²**.

---

Would you like more details on any step? Here are 5 related questions to further your understanding:

1. How is the area of a triangle calculated with different measurements?
2. What happens if the base of the triangle changes?
3. How do you find the perimeter of this shape?
4. Can the same method be applied to other compound shapes?
5. What if the units were in meters instead of centimeters?

**Tip:** When breaking complex shapes into smaller parts, make sure to use the right formula for each section!

Find the area of the shape below. All lengths are in centimetres.

Learn how to find the area of a compound shape consisting of a triangle and a rectangle. In this problem, the triangle has a base of 6 cm and a height of 4 cm, while the rectangle has dimensions of 6 cm by 10 cm. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation