Find the areas of the following kites.

Question

ScanSolve AI Tutor · Accepted Answer

To find the area of a kite, we use the formula:

\text{Area} = \frac{1}{2} \times d_1 \times d_2

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

A)

Identify the lengths of the diagonals for kite A.
The horizontal diagonal ( $d_1$ ) is $3 \text{ cm} + 3 \text{ cm} = 6 \text{ cm}$ .
The vertical diagonal ( $d_2$ ) is $3 \text{ cm} + 5 \text{ cm} = 8 \text{ cm}$ .
Substitute the diagonal lengths into the area formula.
$\text{Area}_A = \frac{1}{2} \times 6 \text{ cm} \times 8 \text{ cm}$
Calculate the area.
$\text{Area}_A = \frac{1}{2} \times 48 \text{ cm}^2 = 24 \text{ cm}^2$
The area of kite A is $\boxed{\text{24 cm}^2}$ .

B)
Identify the lengths of the diagonals for kite B.
The horizontal diagonal ( $d_1$ ) is $4 \text{ cm} + 7 \text{ cm} = 11 \text{ cm}$ .
The vertical diagonal ( $d_2$ ) is $5 \text{ cm} + 5 \text{ cm} = 10 \text{ cm}$ .
Substitute the diagonal lengths into the area formula.
$\text{Area}_B = \frac{1}{2} \times 11 \text{ cm} \times 10 \text{ cm}$
Calculate the area.
$\text{Area}_B = \frac{1}{2} \times 110 \text{ cm}^2 = 55 \text{ cm}^2$
The area of kite B is $\boxed{\text{55 cm}^2}$ .

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