Question

the diagonals of a rhombus are 6 units and 8 units long. what is the area of the rhombus? draw a diagram and show all reasoning.
hint:
the diagonals of a rhombus are perpendicular bisectors of each other. they also bisect the angles of the rhombus. draw a diagram with the information given.
more help:
to \bisect\ means to divide into two equal parts. perpendicular objects form $90^\circ$ angles.

Explanation:

Step1: Recall rhombus area formula

The area of a rhombus is given by $\text{Area} = \frac{1}{2} \times d_1 \times d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals.

Step2: Substitute given diagonal values

Substitute $d_1 = 6$ and $d_2 = 8$ into the formula:
$\text{Area} = \frac{1}{2} \times 6 \times 8$

Step3: Calculate the final value

First compute $6 \times 8 = 48$, then multiply by $\frac{1}{2}$:
$\text{Area} = \frac{1}{2} \times 48 = 24$

(Diagram note: Draw a rhombus with two perpendicular diagonals: one labeled 6 units (split into two 3-unit segments by the intersection) and the other labeled 8 units (split into two 4-unit segments by the intersection). The four right triangles formed each have legs 3 and 4, confirming the rhombus sides are 5 units, but this is not needed for area calculation.)

Answer:

24 square units