Areas of Parallelograms and Triangles Class 9 – If P and Q are congruent figures, then area(P) = area(Q). Two congruent figures will always have equal areas. However, it is not compulsory that two figures equal in area will be congruent. Area of parallelograms lying on same or equal base and parallel lines are equal. If a triangle and a parallelogram are lying on the same base and same parallel lines, then, the area of the triangle is half the area of the parallelogram. Area of triangles lying on the same base and parallel lines are equal. A median divides a triangle into two triangles equal in area. Now, let’s prove that a median divides a triangle into 2 triangles having equal areas. Let us consider a triangle ABC with AD as one of its median. We need to prove that area of triangle ABD = area of triangle ACD.
Let us draw AN perpendicular to BC. Now area of triangle ABD = ½ × base × altitude = ½ BD × AN = ½ CD × AN [Since, BD and CD are equal]
= ½ × base × altitude (of ∆ ACD) = area of triangle ACD
Areas of Parallelograms and Triangles Class 9 Examples