Solved Examples: Finding Rhombus Area with Diagonals (High School Math).

📚 Quick Study Guide

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• Rhombus Definition: A parallelogram with all four sides equal in length.
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• Diagonals: The diagonals of a rhombus bisect each other at right angles.
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• Area Formula (using diagonals): The area of a rhombus is half the product of the lengths of its diagonals. If $d_1$ and $d_2$ are the lengths of the diagonals, then the area $A$ is given by: $A = \frac{1}{2} d_1 d_2$.
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• Units: Remember that the area is expressed in square units (e.g., $cm^2$, $m^2$, $in^2$).

Practice Quiz

1. What is the area of a rhombus with diagonals of length 6 cm and 8 cm?
   1. 24 $cm^2$
   2. 48 $cm^2$
   3. 14 $cm^2$
   4. 36 $cm^2$
2. A rhombus has diagonals of length 10 inches and 12 inches. What is its area?
   1. 60 $in^2$
   2. 120 $in^2$
   3. 22 $in^2$
   4. 100 $in^2$
3. The area of a rhombus is 50 $m^2$. If one diagonal is 10 m, what is the length of the other diagonal?
   1. 5 m
   2. 10 m
   3. 15 m
   4. 20 m
4. What is the area of a rhombus whose diagonals are 7 cm and 9 cm?
   1. 63 $cm^2$
   2. 31.5 $cm^2$
   3. 16 $cm^2$
   4. 23 $cm^2$
5. A rhombus has an area of 48 $cm^2$. One of its diagonals is 12 cm. What is the length of the other diagonal?
   1. 4 cm
   2. 6 cm
   3. 8 cm
   4. 10 cm
6. Find the area of a rhombus if its diagonals measure 5 inches and 11 inches.
   1. 55 $in^2$
   2. 27.5 $in^2$
   3. 16 $in^2$
   4. 33 $in^2$
7. The diagonals of a rhombus are in the ratio 2:3. If the area of the rhombus is 27 $m^2$, find the lengths of the diagonals.
   1. 6 m and 9 m
   2. 3 m and 4.5 m
   3. 9 m and 13.5 m
   4. 4 m and 6 m