If the length of a diagonal of a quadrilateral is 10 cm and lengths of the perpendiculars on it from opposite vertices are 4 cm and 6 cm, then area of quadrilateral is

1. 100 cm²

2. 200 cm²

3. 50 cm²

4. None of these.

Let ABCD be the quadrilateral with diagonal BD.

Let AM and CN be the perpendiculars from A and C on diagonal BD.

From figure,

BD divides quadrilateral in two triangles.

Area of △ABD = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × BD × AM

= $\dfrac{1}{2}$ × 10 × 4

= 20 cm².

Area of △BCD = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × BD × CN

= $\dfrac{1}{2}$ × 10 × 6

= 30 cm².

Area of quadrilateral = Area of △ABD + Area of △BCD

= 20 + 30 = 50 cm².

Hence, Option 3 is the correct option.