Examples

Areas of Parallelograms and Triangles
Serial order wise

### Transcript

Example 2 (Method 1) If a triangle and a parallelogram are on the same base and between the same parallels, then prove that area of triangle is equal to half the area of parallelogram. Given: A parallelogram ABCD and ABP on the same base AB and between the same parallels To prove: Area of triangle is equal to half the area of parallelogram. ar ( ABP ) = 1/2 ar (ABCD) Construction: Join DP Let DM AB & PN AB Proof: Example 2 (Method 2) If a triangle and a parallelogram are on the same base and between the same parallels, then prove that area of triangle is equal to half the area of parallelogram. Given: A parallelogram ABCD and ABP on the same base AB and between the same parallels PC & AB To prove: Area of triangle is equal to half the area of parallelogram. ar ( ABP ) = 1/2 ar (ABCD) Proof: In parallelogram ABCD, AB CD So, PC AB We draw a line BQ parallel to AP , i.e. , BQ AP Since BQ AP & PQ AB, Both pairs of opposite sides are parallel ABQP is a parallelogram Parallelograms ABQP & ABCD are on the same base AB and between the same parallel lines AB & PC Area(ABQP) = Area(ABCD) In parallelogram ABQP, BP is the diagonal So, ABP QBP Area( ABP) = Area( QBP) Now, Area( ABP) = Area( QBP) = 1/2 Area(ABQP) Area( ABP) = 1/2 Area(ABQP) Area( ABP) = 1/2 Area(ABCD) Hence proved

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.