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ISEE Upper Level Math : How to find the area of a rhombus

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Example Questions

Example Question #284 : Geometry

Two diagonals of a rhombus have lengths of (t+1) $\displaystyle (t+1)$ and (t-1) $\displaystyle (t-1)$ . Give the area in terms of $\displaystyle t$ .

Possible Answers:

t^2+1 $\displaystyle t^2+1$

$\frac{t^2-1}{2}$ $\displaystyle \frac{t^2-1}{2}$

t^2-1 $\displaystyle t^2-1$

$\frac{t^2+1}{2}$ $\displaystyle \frac{t^2+1}{2}$

t^2 $\displaystyle t^2$

Correct answer:

$\frac{t^2-1}{2}$ $\displaystyle \frac{t^2-1}{2}$

Explanation:

The formula for the area of a rhombus is

$Area=\frac{d_{1}d_{2}}{2}$ $\displaystyle Area=\frac{d_{1}d_{2}}{2}$ ,

where $d_{1}$ $\displaystyle d_{1}$ is the length of one diagonal and $d_{2}$ $\displaystyle d_{2}$ is the length of the other diagonal.

$Area=\frac{d_{1}d_{2}}{2}=\frac{(t-1)(t+1)}{2}=\frac{t^2-1}{2}$ $\displaystyle Area=\frac{d_{1}d_{2}}{2}=\frac{(t-1)(t+1)}{2}=\frac{t^2-1}{2}$

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Example Question #1 : Rhombuses

A rhombus has side length $4\ cm$ $\displaystyle 4\ cm$ , and one of the interior angles is $30^{\circ}$ $\displaystyle 30^{\circ}$ . Give the area of the rhombus.

Possible Answers:

$8\ cm^2$ $\displaystyle 8\ cm^2$

$12\ cm^2$ $\displaystyle 12\ cm^2$

$9\ cm^2$ $\displaystyle 9\ cm^2$

$6\ cm^2$ $\displaystyle 6\ cm^2$

$10\ cm^2$ $\displaystyle 10\ cm^2$

Correct answer:

$8\ cm^2$ $\displaystyle 8\ cm^2$

Explanation:

The area of a rhombus can be determined by the following formula:

$Area=s^2sin\alpha$ $\displaystyle Area=s^2sin\alpha$ ,

where $\displaystyle s$ is the length of any side and $\alpha$ $\displaystyle \alpha$ is any interior angle.

$Area=s^2sin\alpha=4^2\times sin30^{\circ}=16\times \frac{1}{2}=8\ cm^2$ $\displaystyle Area=s^2sin\alpha=4^2\times sin30^{\circ}=16\times \frac{1}{2}=8\ cm^2$

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Example Question #291 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Find the area of a rhombus with one diagonal having a length of 12in and the other having a length two times the first diagonal.

Possible Answers:

$100\text{in}^2$ $\displaystyle 100\text{in}^2$

$288\text{in}^2$ $\displaystyle 288\text{in}^2$

$144\text{in}^2$ $\displaystyle 144\text{in}^2$

$121\text{in}^2$ $\displaystyle 121\text{in}^2$

$48\text{in}^2$ $\displaystyle 48\text{in}^2$

Correct answer:

$144\text{in}^2$ $\displaystyle 144\text{in}^2$

Explanation:

To find the area of a rhombus, we will use the following formula:

$A = \frac{pq}{2}$ $\displaystyle A = \frac{pq}{2}$

where p and q are the lengths of the diagonals of the rhombus.

Now, we know one diagonal has a length of 12in. We also know the other diagonal is two times the first diagonal. Therefore, the second diagonal is 24in.

Knowing this, we can substitute into the formula. We get

$A = \frac{12\text{in} \cdot 24\text{in}}{2}$ $\displaystyle A = \frac{12\text{in} \cdot 24\text{in}}{2}$

$A = \frac{288\text{in}^2}{2}$ $\displaystyle A = \frac{288\text{in}^2}{2}$

$A = 144\text{in}^2$ $\displaystyle A = 144\text{in}^2$

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ISEE Upper Level Math : How to find the area of a rhombus

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #284 : Geometry

Example Question #1 : Rhombuses

Example Question #291 : Isee Upper Level (Grades 9 12) Mathematics Achievement

All ISEE Upper Level Math Resources

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