https://file.aiquickdraw.com/mathbot/file/1734629437900t7hlf3z5.jpg

Let us solve the problem step by step.

### Problem Analysis:
1. **Rectangle:** The area of a rectangle is given by:
   \[
   \text{Area} = \text{Length} \times \text{Width}.
   \]
   Here, the rectangle's dimensions are \( 8 \, \text{cm} \) (height) and \( 5 \, \text{cm} \) (width). Thus, the area of the rectangle is:
   \[
   \text{Area}_{\text{rect}} = 8 \times 5 = 40 \, \text{cm}^2.
   \]

2. **Triangle:** The area of a triangle is given by:
   \[
   \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}.
   \]
   Here, the triangle's height is \( 5 \, \text{cm} \), and the base is \( d \, \text{cm} \). The area of the triangle is:
   \[
   \text{Area}_{\text{tri}} = \frac{1}{2} \times d \times 5 = \frac{5d}{2} \, \text{cm}^2.
   \]

3. Since the two areas are equal, we can set:
   \[
   \text{Area}_{\text{rect}} = \text{Area}_{\text{tri}}.
   \]

### Solving the Equation:
Equating the two areas:
\[
40 = \frac{5d}{2}.
\]

Multiply through by 2 to eliminate the fraction:
\[
80 = 5d.
\]

Divide both sides by 5:
\[
d = \frac{80}{5} = 16.
\]

### Final Answer:
The value of \( d \) is:
\[
\boxed{16 \, \text{cm}}.
\]

Let me know if you want further clarifications!

---

### Related Questions:
1. What is the general formula for calculating the area of a triangle?
2. How can you verify that two shapes have the same area mathematically?
3. If the base \( d \) of the triangle was doubled, how would its area change?
4. What happens to the rectangle's area if one side is increased by 50%?
5. How do we calculate the areas of other polygons like trapeziums?

### Tip:
Always include units in your calculations to ensure clarity and precision in math problems.

The rectangle and triangle below have the same area. Calculate d, giving your answer in centimetres (cm).

Learn how to calculate the base of a triangle when it has the same area as a rectangle. This problem involves area calculations, geometry, and solving equations. Suitable for middle school students (Grades 6-8).

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