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In ΔABC, D is the midpoint of AB. P is any point on BC, and Q is a point on AB such that CQ || PD. PQ is joined (figure). Prove that
Area (ΔBPQ) = \(\frac{1}{2}\) Area (ΔABC).

Given a square ABCD, let P be a point within it. Join PA, PB, PC, PD (figure). What is the ration of the areas of the red region (ΔPAB and ΔPD) and the green region (ΔPBC and ΔPDA)?

In ΔABC, the midpoint of BC is D(figure). Median AD is drawn. P is any point on AD. Show that
area(ΔABP) = area(ΔACP).

If the mid-points of the sides of a 4-gon(also known as a quadrilateral, but we prefer to call it '4-gon') are joined in order, prove that the area of the parallelogram thus formed will be half of the area of the given 4-gon.

O is any point on the diagonal PR of a parallelogram PQRS. Prove that the areas of triangle PSO and PQO are equal.

One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm\(^2\), find the length of the shorter diagonal.

The sides of a triangular plot are in the ratio 3 : 5 : 7; its perimeter is 300m. Find its area.

Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm.

The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium.

Find the area of triangle ADE in the given figure.