(ii) length of the diagonal up to 2 decimal places.
7. Find the aren of a rhombus ABCD in which cach side measures 30 cm and one of its dingonal is
48 cm .
8. An iron sheet is rhombus in shape. The measure of its side is 15 cm and one of its diagonal in

Question

UpStudy AI · Accepted Answer

To solve the problems regarding the rhombus, we will follow these steps:

### Problem 7: Area of a Rhombus

**Known Conditions:**
- Each side of the rhombus (s) = 30 cm
- One diagonal (d₁) = 48 cm

**Step 1: Find the other diagonal (d₂)**

In a rhombus, the diagonals bisect each other at right angles. We can use the Pythagorean theorem to find the length of the other diagonal.

Let $$ d_2 $$ be the length of the other diagonal. The relationship can be expressed as:
$$
s^2 = \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2
$$

Substituting the known values:
$$
30^2 = \left(\frac{48}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2
$$

Calculating:
$$
900 = 24^2 + \left(\frac{d_2}{2}\right)^2
$$
$$
900 = 576 + \left(\frac{d_2}{2}\right)^2
$$
$$
\left(\frac{d_2}{2}\right)^2 = 900 - 576
$$
$$
\left(\frac{d_2}{2}\right)^2 = 324
$$
$$
\frac{d_2}{2} = 18 \quad \Rightarrow \quad d_2 = 36
$$

**Step 2: Calculate the area (A) of the rhombus**

The area of a rhombus can be calculated using the formula:
$$
A = \frac{d_1 \cdot d_2}{2}
$$

Substituting the values:
$$
A = \frac{48 \cdot 36}{2}
$$
$$
A = \frac{1728}{2} = 864 \text{ cm}^2
$$

### Problem 8: Area of a Rhombus

**Known Conditions:**
- Each side of the rhombus (s) = 15 cm
- One diagonal (d₁) = unknown (not provided in the prompt)

Since the second diagonal is not provided, we cannot calculate the area without additional information. If you can provide the length of the second diagonal or any other relevant information, I can help you find the area.

### Summary of Results
- **Area of Rhombus ABCD**: $$ 864 \text{ cm}^2 $$
- **Area of the iron sheet rhombus**: Requires additional information about the diagonals.
- **Problem 7**: The area of rhombus ABCD is 864 cm². - **Problem 8**: Cannot determine the area without the length of the second diagonal.

(ii) length of the diagonal up to 2 decimal places.
7. Find the aren of a rhombus ABCD in which cach side measures 30 cm and one of its dingonal is
48 cm .
8. An iron sheet is rhombus in shape. The measure of its side is 15 cm and one of its diagonal in

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Problem 7: Area of a Rhombus

Problem 8: Area of a Rhombus

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(ii) length of the diagonal up to 2 decimal places. 7. Find the aren of a rhombus ABCD in which cach side measures 30 cm and one of its dingonal is 48 cm . 8. An iron sheet is rhombus in shape. The measure of its side is 15 cm and one of its diagonal in

Solución de inteligencia artificial de Upstudy

Responder

Solución

Problem 7: Area of a Rhombus

Problem 8: Area of a Rhombus

Summary of Results

Beyond the Answer

preguntas relacionadas

Latest Geometry Questions

(ii) length of the diagonal up to 2 decimal places.
7. Find the aren of a rhombus ABCD in which cach side measures 30 cm and one of its dingonal is
48 cm .
8. An iron sheet is rhombus in shape. The measure of its side is 15 cm and one of its diagonal in