Area of triangle APD?

A normal-level "Area" problem.Wherever P sits on BC, the answer is the same. Try sliding P to the very end in the figure.

GivenParallelogram ABCD has area 48 cm². P is a point on side BC.

Hints

1. Take AD as the base of triangle APD. AD is also one side of the parallelogram.
2. The height is the perpendicular distance from P up to AD. Let's draw it as a dotted line.
3. The parallelogram's height is also the perpendicular distance from BC to AD. Since AD and BC are parallel, the two heights are equal (see the marks).
4. So wherever you slide P along BC, the base and the height never change. P's position has nothing to do with the answer.
5. Same base, same height. The only difference is the ÷ 2 in the formula. So the triangle is exactly half of the parallelogram.
6. Put the two formulas side by side and the only difference is clearly ÷ 2.
7. 48 ÷ 2 gives the answer.

Answer 24cm²

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