Calculate Deltoid Area: Using Diagonals AC=7cm and DB=5cm

Question

Look at the deltoid ABCD below.

Given in cm:

AC = 7

DB = 5

Calculate the area of the deltoid.

00:00 Calculate the area of the kite

00:03 We'll use the formula to calculate the area of a kite

00:08 (diagonal times diagonal) divided by 2

00:13 We'll substitute the appropriate values according to the given data and solve for the area

00:27 And this is the solution to the question

To find the area of the deltoid $ABCD$ , we will use the area formula for a deltoid:

$A = \frac{1}{2} \times d_1 \times d_2$

where $d_1$ and $d_2$ are the lengths of the diagonals.

Given:

Substitute the given lengths into the formula:

$A = \frac{1}{2} \times 7 \times 5$

$A = \frac{1}{2} \times 35$

$A = 17.5 \, \text{cm}^2$

Therefore, the area of the deltoid is $17.5 \, \text{cm}^2$ .

17.5 cm².