In parallelogram ABCD, P is a point on DC. If the area of triangle APB is 30 cm², what is the area of parallelogram ABCD?

Parallelograms PQRS and TURS are on the same base SR and between the same parallels PU and SR. If the area of PQRS is 50 cm², what is the area of TURS?

In trapezium ABCD, AB // DC. If the area of triangle ADC is 25 cm², what is the area of triangle BDC?

In the figure, PQRS is a parallelogram and T is a point on SR. The area of triangle PQT is 40 cm². Find the area of triangle PST + area of triangle QRT.

ABCD is a parallelogram. P is any point on the diagonal AC. Prove that the area of triangle APD is equal to the area of triangle APB.

The diagonals of a trapezium ABCD intersect at O, with AB // DC. Prove that the area of triangle AOD is equal to the area of triangle BOC.

The vertices of a triangle PQR lie on the sides of a triangle ABC such that P, Q, and R are the midpoints of AB, BC, and CA respectively. Prove that the area of triangle PQR is 41​ of the area of triangle ABC.

In parallelogram ABCD, E is the midpoint of AD. Prove that the area of triangle ABE is equal to the area of triangle EBC.

ABCD is a parallelogram. A line through B parallel to the diagonal AC meets DC produced at E. Prove that the area of triangle ADE is equal to the area of parallelogram ABCD.

In triangle ABC, D is the midpoint of BC. E is the midpoint of AD. Prove that the area of triangle ABE is 41​ of the area of triangle ABC.

Let P be any point on the median AD of a triangle ABC. Prove that the area of triangle APB is equal to the area of triangle APC.

ABCD is a quadrilateral. A line drawn through D parallel to AC meets BC produced at E. Prove that the area of quadrilateral ABCD is equal to the area of triangle ABE.

In triangle ABC, X is a point on AB. A line is drawn through X parallel to BC, meeting AC at Y. Prove that the area of triangle ABY is equal to the area of triangle ACX.

PQRS is a parallelogram. T is a point on PQ. The area of triangle STR is 75 cm². Find the area of the parallelogram PQRS.

The medians AD, BE, and CF of a triangle ABC intersect at G. Prove that the area of triangle AGB is equal to the area of triangle BGC.