Calculate the Diagonal Length in a Deltoid: Given Area 32 cm² and AC = 8 cm

Question

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

00:00 Calculate diagonal DB

00:03 We'll use the formula for calculating the area of a kite

00:06 (diagonal times diagonal) divided by 2

00:10 We'll substitute appropriate values and solve for BD

00:17 Multiply by 2 to eliminate the fraction

00:26 Isolate BD

00:30 And this is the solution to the question

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

$\frac{8\cdot DB}{2}=32$

We reduce the 8 and the 2:

$4DB=32$

Divide by 4

$DB=8$

8 cm