The deltoid below has an area of 60 cm².
What is the value of X?
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The deltoid below has an area of 60 cm².
What is the value of X?
To solve the problem, we need to remember the formula for the area of a rhombus:
The product of the diagonals multiplied together and then divided by 2.
Let's substitute in our data into the formula:
(8*X) = 60
2
Note that we can simplify the fraction, thus eliminating the denominator:
4X = 60
Let's finally divide the equation by 4 to get our answer:
X = 15
15
Look at the deltoid in the figure:
What is its area?
A rectangle uses length × width, but a rhombus uses diagonals! The formula is . This is because diagonals in a rhombus are perpendicular.
Diagonals are the lines that cross through the center of the rhombus from opposite corners. In this problem, the vertical line (height 8) and horizontal line (length X) are the diagonals.
When diagonals cross perpendicularly, they create 4 right triangles. The total area is twice the area of the rectangle formed by the diagonals, so we divide by 2.
The diagonal formula is the standard method for rhombus area. While there are other approaches using trigonometry, this formula is the most direct for this type of problem.
That's fine! Many geometry problems have decimal solutions. Just make sure to check your work by substituting back into the area formula.
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