To determine the area of a kite-shaped logo, we can use the formula for the area of a kite, which is given by:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{d}_1 \times \text{d}_2 \][/tex]
where [tex]\(\text{d}_1\)[/tex] and [tex]\(\text{d}_2\)[/tex] are the lengths of the diagonals of the kite. In this problem, the width of the logo represents one diagonal ([tex]\(\text{d}_1 = 12 \text{ cm}\)[/tex]), and the height of the logo represents the other diagonal ([tex]\(\text{d}_2 = 16 \text{ cm}\)[/tex]).
By substituting the given values into the formula, we get:
[tex]\[
\text{Area} = \frac{1}{2} \times 12 \text{ cm} \times 16 \text{ cm}
\][/tex]
Now, calculate the product of the diagonals:
[tex]\[
12 \times 16 = 192 \text{ cm}^2
\][/tex]
Next, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} \times 192 \text{ cm}^2 = 96 \text{ cm}^2
\][/tex]
Therefore, the area of the kite-shaped logo is:
[tex]\[
96 \text{ cm}^2
\][/tex]
Among the given options (48 sq cm, 96 sq cm, 144 sq cm, 192 sq cm), the correct answer is:
[tex]\[
96 \text{ sq. cm}
\][/tex]
