The diagonals of a rhombus are 12 cm and 9 cm and its height is 5 cm. Find the area of the rhombus.?

Question

Answer

Area of rhombus = 1/2(d1×d2)
= 1/2(12×9)
= 1/2× 108
=54
IN THIS ,HEIGHT IS NOT REQUIRED BUT GIVEN IN QUESTION. SO, THIS IS A RIGHT ANSWER

Answer

Area of rhombus=1/2 (d1xd2)

d1 = 12cm
d2 = 9cm

so
a/q

1/2 (12×9)
1/2×108
so, 54cm2

so, area = 54cm^....

Answer

Area of rhombus=1/2(d1×d2)
1/2(12×9)
1/2×108=54

Answer

**Problem Statement:**
We are given a rhombus with diagonals of length 12 cm and 9 cm, and a height of 5 cm. We need to find the area of the rhombus.

**Solution:**
To find the area of the rhombus, we can use the formula:

Area = (diagonal1 * diagonal2) / 2

However, before we can use this formula, we need to find the length of the diagonals.

**Finding the Length of the Diagonals:**

From the given information, we know that the diagonals of the rhombus are 12 cm and 9 cm. Let's assume the longer diagonal is diagonal1 and the shorter diagonal is diagonal2.

We can divide the rhombus into two congruent right triangles. The height of the rhombus is the altitude of these right triangles.

Using the Pythagorean theorem, we can find the length of the base of each right triangle:

base = √(diagonal^2 - height^2)

For the longer diagonal (diagonal1):
base1 = √(12^2 - 5^2)
= √(144 - 25)
= √(119)
≈ 10.92 cm

For the shorter diagonal (diagonal2):
base2 = √(9^2 - 5^2)
= √(81 - 25)
= √(56)
≈ 7.48 cm

Now we have the lengths of the diagonals and can calculate the area of the rhombus.

**Calculating the Area of the Rhombus:**

Using the formula for the area of a rhombus:

Area = (diagonal1 * diagonal2) / 2

Area = (12 * 9) / 2
= 108 / 2
= 54 cm²

Therefore, the area of the rhombus is 54 cm².

**Summary:**
- Given a rhombus with diagonals of length 12 cm and 9 cm, and a height of 5 cm.
- To find the area of the rhombus, we first need to find the lengths of the diagonals.
- Using the Pythagorean theorem, we find the lengths of the base of the right triangles formed by the diagonals and the height.
- The length of the longer diagonal (diagonal1) is approximately 10.92 cm, and the length of the shorter diagonal (diagonal2) is approximately 7.48 cm.
- Using the formula for the area of a rhombus, we calculate the area to be 54 cm².

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