In rectangle ABCD, side AB = 12 cm. The distance from the point of intersection of the diagonals to this side is 8 cm. Find the area of triangle ABCD.
1. The distance from the point of intersection of the diagonals to the side AB of the rectangle is calculated by drawing a perpendicular to this side.
2. The perpendicular is the middle line of triangle ABD, since it is parallel to AD and drawn from the middle of the diagonal BD.
3. The middle line of the triangle is equal to ABD half of the side AD. Therefore, AD = 8 x 2 = 16 centimeters.
4. Calculate the area of the rectangle ABCD:
16 x 12 = 192 cm ^ 2.
Answer: the area of the rectangle ABCD is 192 cm ^ 2.
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