Question

P is a point on side AB of parallelogram ABCD. Which of the following is true?

1. Area of ΔAPD = `1/4` area || gm ABCD
2. Area of ΔPDC = `1/2` area || gm ABCD
3. Area of ΔAPD + area of ΔPBC = `1/2` parallelogram ABCD

विकल्प

• only A

• only B

• A and B

• B and C

Answer 1

B and C

Explanation:

Statement (B) is True: 

Imagine sliding point P along the top line AB. No matter where P is on AB, the triangle ΔPDC always has the same base (DC) and the same height as the parallelogram ABCD (the distance between lines AB and DC). When a triangle and a parallelogram share the same base and height, the triangle's area is always half the parallelogram's area. So, Area ΔPDC = `1/2` Area || gm ABCD.

Statement (C) is True:

Think about the three triangles inside the parallelogram: ΔPDC, ΔAPD, ΔPBC and ΔPDC. These three triangles together make up the whole parallelogram. We just learned that Area ΔPDC is half the area of the parallelogram. This means the other two triangles combined (ΔAPD and ΔPBC) must also make up the other half of the parallelogram’s area. So, Area ΔAPD + Area ΔPBC = `1/2` Area || gm ABCD.