Questions: Find the area of the rhombus. 64 sqrt(3) m^2 48 sqrt(3) m^2 32 sqrt(3) m^2

Transcript text: Quiz: Areas of Special Quadrilat CR Geometry B (GP) 24-25 / 3:Area 3. Find the area of the rhombus. $64 \sqrt{3} \mathrm{~m}^{2}$ $48 \sqrt{3} \mathrm{~m}^{2}$ $32 \sqrt{3} \mathrm{~m}^{2}$

Solution

Solution Steps

Step 1: Identify the given dimensions

The problem provides the lengths of the diagonals of the rhombus. One diagonal is $4\sqrt{3}$ meters and the other is 4 meters.

Step 2: Recall the formula for the area of a rhombus

The area $A$ of a rhombus can be calculated using the formula: \[ A = \frac{1}{2} \times d_1 \times d_2 \] where $d_1$ and $d_2$ are the lengths of the diagonals.

Step 3: Substitute the given values into the formula

Substitute $d_1 = 4\sqrt{3}$ meters and $d_2 = 4$ meters into the formula: \[ A = \frac{1}{2} \times 4\sqrt{3} \times 4 \]

Step 4: Simplify the expression

Calculate the product inside the formula: \[ A = \frac{1}{2} \times 16\sqrt{3} \] \[ A = 8\sqrt{3} \]