Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 8 Area of Plane Figures between Parallel Lines

Name two parallelograms of equal area on one base

Answer: ABEF and ABCD

💡 What it's asking: We must find two parallelograms with equal area. Shapes on the same base and between the same pair of parallel lines have equal area.

1. 1Read the arrow marks: AF ∥ BE and AD ∥ BC.
2. 2A four-sided shape with both pairs of opposite sides parallel is a parallelogram, so ABEF and ABCD are parallelograms.
3. 3Both have the same base AB.
4. 4Both lie between the same two parallel lines, so they have the same height.
5. 5Same base × same height gives the same area, so ABEF and ABCD are equal in area.

✅ Picture sliding the top side along its line: the shape leans more but its base and height do not change, so the area stays the same.

Distance between parallels from parallelogram area

Answer: 12 cm

💡 What it's asking: We know the area and the base, and need the distance between the parallel lines, which is the height. Use area = base × height backwards.

1. 1Area of a parallelogram = base × perpendicular height (height measured at a right angle to the base).
2. 2Put in the numbers: 72 = 6 × height.
3. 3Divide both sides by 6: height = 72 ÷ 6 = 12.
4. 4The distance between the parallel lines is the height, so it is 12 cm.

✅ 6 × 12 = 72, which matches the given area of 72 cm².

Equal parallelograms on a shared base

Parallelogram equal to a rectangle on the same base

Name two parallelograms of equal area

Triangle on the base of a parallelogram

Equal triangles on base AB; triangle as half a parallelogram

Equal triangles in a trapezium with crossing diagonals

Sum of two triangles beside a central triangle