Example 1 - Areas of Parallelograms and Triangles

Transcript

Example 1 In given figure, ABCD is a parallelogram and EFCD is a rectangle. Also, AL ⊥ DC. Prove that (i) ar (ABCD) = ar (EFCD) Given that ABCD is a parallelogram Hence AB ∥ CD We know that a rectangle is also a parallelogram, so EFCD is also a parallelogram So, EF ∥ CD Since AB ∥ CD and EF ∥ CD we can say that EB ∥ CD Now, ABCD & EFDC are two parallelograms with the same base CD and between the same parallels EB & CD ∴ ar (ABCD) = ar (EFCD) Example 1 In Fig., ABCD is a parallelogram and EFCD is a rectangle. Also, AL ⊥ DC. Prove that (ii) ar (ABCD) = DC × AL ABCD is a parallelogram with Base DC and altitude AL Now, Area of a parallelogram = Base × Corresponding altitude ∴ ar (ABCD) = DC × AL Hence proved