The diagonal of four gons ABCD is mutually perpendicular, AC = 12 cm, BD = 15 cm.
| September 18, 2021 | education
The diagonal of four gons ABCD is mutually perpendicular, AC = 12 cm, BD = 15 cm. Find the area of a quadrilateral whose vertices are the midpoints of the sides of this quadrilateral.
According to the formula for the area of an arbitrary convex quadrilateral:
s = 1/2 * d1 * d2 * sinA (angle between diagonals)
If the diagonals are perpendicular then the angle between them is 90 degrees, then
s = 1/2 * 12 * 15 * sin 90 = 0.5 * 12 * 15 * 1 = 90cm2
answer area 90 cm2
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