Shown below is the deltoid ABCD.
The diagonal AC is 3 cm long.
The area of the deltoid is 18 cm².
Calculate the diagonal DB.
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Shown below is the deltoid ABCD.
The diagonal AC is 3 cm long.
The area of the deltoid is 18 cm².
Calculate the diagonal DB.
The goal here is to find the diagonal of the deltoid. Given:
We utilize the formula relating the diagonals and area of a deltoid:
Here, cm (given as diagonal ) and the area is given as 18 cm. We are solving for .
Substituting the known values into the formula:
First, multiply both sides by 2 to clear the fraction:
Now, solve for by dividing both sides by 3:
Therefore, the diagonal of the deltoid is .
12 cm
Indicate the correct answer
The next quadrilateral is:
A deltoid is a kite-shaped quadrilateral with two pairs of adjacent equal sides. Unlike rectangles or triangles, its area formula specifically uses the diagonals, not sides or base and height.
The formula comes from dividing the deltoid into four triangles using both diagonals. Each triangle's area adds up to half the rectangle formed by the diagonals.
It doesn't matter! The deltoid area formula works the same way regardless of which diagonal you call d₁ or d₂. Just substitute the known diagonal length and solve for the unknown one.
No, you need at least one diagonal length to use this formula. With just the area, you'd have one equation with two unknowns, which has infinitely many solutions.
That's perfectly valid! Real-world measurements often result in decimal lengths. Just make sure your calculation is correct by substituting back into the area formula to verify.
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