How to find the height of a rhombus?
Understand the Problem
The question is asking how to determine the height of a rhombus. To solve this, one can use the formula that incorporates the area of the rhombus and its base, or relate the height to the diagonals if those are known.
Answer
The height of the rhombus is given by the formula $h = \frac{d_1 \times d_2}{2b}$.
Answer for screen readers
The height of the rhombus can be calculated using the formula: $$ h = \frac{d_1 \times d_2}{2b} $$
Steps to Solve
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Identify the Area Formula The area 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.
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Express Height in Terms of Area The area can also be expressed in terms of the base (which is any side of the rhombus) ( b ) and the height ( h ): $$ A = b \times h $$
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Set the Two Formulas Equal Since both expressions represent the same area, we can set them equal to each other: $$ \frac{1}{2} \times d_1 \times d_2 = b \times h $$
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Solve for Height Rearranging the equation helps us solve for height ( h ): $$ h = \frac{d_1 \times d_2}{2b} $$
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Substitute Known Values If you have specific values for the diagonals ( d_1 ) and ( d_2 ), and the length of a side ( b ), substitute them into the equation to find the height.
The height of the rhombus can be calculated using the formula: $$ h = \frac{d_1 \times d_2}{2b} $$
More Information
This formula shows that the height of a rhombus is directly related to its diagonals and the length of a side. Knowing just one of these sets of measurements allows us to calculate the others.
Tips
- Forgetting to square the diagonals when using the area formula.
- Confusing the base of the rhombus with the lengths of its sides or diagonals.
- Not substituting correctly when plugging values into the formula.
