The problem asks for the area of a quadrilateral ABCD where specific side lengths are equal: AB = BC and CD = DA. A quadrilateral with two distinct pairs of equal-length adjacent sides is known as a kite.
In this kite ABCD:
The diagonals provided are AC = 6 cm and BD = 12 cm.
The area of a kite can be calculated using the lengths of its diagonals. The formula for the area (A) of a kite is:
\( A = \frac{1}{2} \times d_1 \times d_2 \)
where \(d_1\) and \(d_2\) represent the lengths of the two diagonals.
We are given the lengths of the diagonals:
Now, we substitute these values into the area formula:
\( A = \frac{1}{2} \times AC \times BD \)
\( A = \frac{1}{2} \times 6 \text{ cm} \times 12 \text{ cm} \)
First, multiply the lengths of the diagonals:
\( 6 \text{ cm} \times 12 \text{ cm} = 72 \text{ square cm} \)
Then, multiply the result by \(\frac{1}{2}\):
\( A = \frac{1}{2} \times 72 \text{ square cm} \)
\( A = 36 \text{ square cm} \)
The calculated area of the quadrilateral ABCD is 36 square cm.
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