The area of a rhombus is 28 cm² and its perimeter is 28 cm. Find its altitude.

To solve this problem, we need to use the formulas for the area and perimeter of a rhombus.

### Step 1: Use the perimeter to find the side length.
The perimeter \( P \) of a rhombus is given by:

\[
P = 4s
\]

where \( s \) is the length of a side. Given that the perimeter is 28 cm, we can solve for \( s \):

\[
28 = 4s \quad \Rightarrow \quad s = \frac{28}{4} = 7 \, \text{cm}
\]

So, each side of the rhombus is 7 cm.

### Step 2: Use the area formula to find the altitude.
The area \( A \) of a rhombus can also be expressed as:

\[
A = s \times h
\]

where \( h \) is the altitude (the perpendicular distance between two opposite sides). Given that the area is 28 cm² and the side length \( s \) is 7 cm, we can solve for \( h \):

\[
28 = 7 \times h \quad \Rightarrow \quad h = \frac{28}{7} = 4 \, \text{cm}
\]

### Final Answer:
The altitude of the rhombus is \( 4 \, \text{cm} \).

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Would you like further details or have any other questions?

Here are some related questions to explore further:
1. How do you calculate the area of a rhombus using its diagonals?
2. What is the relationship between the diagonals of a rhombus?
3. How does the formula for the area of a rectangle differ from that of a rhombus?
4. What is the significance of the altitude in different quadrilaterals?
5. How can you calculate the diagonals of a rhombus given its side length and altitude?

**Tip:** In a rhombus, the diagonals bisect each other at right angles and play a key role in determining its area if the side lengths aren't directly available.

Learn how to calculate the altitude of a rhombus when the area is 28 cm² and the perimeter is 28 cm. This geometry problem involves using the formulas for perimeter and area. Suitable for students in Grades 6-8.

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