What is the area of rhombus ABCD?
Understand the Problem
The question is asking for the area of a rhombus, specifically labeled ABCD. To solve this, we will need to use the formula for the area of a rhombus, which can be calculated using the lengths of its diagonals or its base and height.
Answer
The area of the rhombus is \( A = \frac{1}{2} d_1 d_2 \).
Answer for screen readers
The area of the rhombus ABCD is expressed as ( A = \frac{1}{2} d_1 d_2 ), where ( d_1 ) and ( d_2 ) are the lengths of the diagonals.
Steps to Solve
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Identify the Formula The area ( A ) of a rhombus can be calculated using the lengths of its diagonals ( d_1 ) and ( d_2 ) with the formula: $$ A = \frac{1}{2} d_1 d_2 $$
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Measure the Diagonals Make sure you have the lengths of both diagonals ( d_1 ) and ( d_2 ). If the problem provides these lengths, you can proceed. If not, you will need to find or measure them.
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Substitute the Values Once you have the values for ( d_1 ) and ( d_2 ), substitute them into the area formula. For example, if ( d_1 = 10 ) and ( d_2 = 5 ): $$ A = \frac{1}{2} \times 10 \times 5 $$
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Calculate the Area Perform the multiplication and division to find the area. Using the earlier example: $$ A = \frac{1}{2} \times 10 \times 5 = \frac{50}{2} = 25 $$
The area of the rhombus ABCD is expressed as ( A = \frac{1}{2} d_1 d_2 ), where ( d_1 ) and ( d_2 ) are the lengths of the diagonals.
More Information
The area of a rhombus can also be found using the base and height, but using the diagonals is typically more straightforward when those measurements are known. Fun fact: A rhombus is a special type of parallelogram where all sides are equal, and its angles can vary.
Tips
- Not using the correct formula for the area of a rhombus.
- Confusing the lengths of the sides with the lengths of the diagonals.
- Forgetting to divide the product of the diagonals by 2.
