Year 7 Maths • AC9M7M01 • Homework
Area of Triangles and Parallelograms
Show formulas, substitutions, units and reasoning. Use perpendicular height in every area calculation.
Part A — 5 × 2-mark questions
- Calculate the area of a triangle with base 18 cm and perpendicular height 11 cm.
- A parallelogram has base 14 m and perpendicular height 9 m. Find its area.
- Explain why sliding the top vertex of a triangle parallel to its base, while keeping the same base and perpendicular height, does not change area.
- A rectangle has area 96 cm² and is cut along a diagonal. Find the area of each triangle and justify your answer.
- Shade cloth costs $15 per m². A triangular sail has base 10 m and height 6 m. Find the total material cost.
Part B — 5 × 5-mark questions
- A 20 cm × 12 cm rectangle contains a triangle using the full base and full height. Calculate both areas, derive the triangle formula from the rectangle, and explain why the triangle is exactly half the rectangle.
- A parallelogram has base 16 cm and height 9 cm. Its top edge slides horizontally in dynamic geometry software. Calculate area, describe how the shape changes, explain why area remains constant, and identify which measurements matter.
- A triangular shade sail must have area 40 m². Give three different base-height pairs, explain why many pairs are possible, and describe how increasing base changes the required height.
- A parallelogram has area 150 cm² and base 25 cm. Find its height, explain why the slanted side is irrelevant to area, and describe a cut-and-rearrange argument that turns it into a rectangle.
- A triangle has area 72 cm² and height 12 cm. Find its base, then explain how two copies could form a parallelogram and use that construction to confirm the triangle-area formula.
Part C — Enrichment investigation
A ranger models triangular river-bank sections with fixed base 30 m while seasonal water levels change the perpendicular height. For heights 4, 7, 10, 13 and 16 m: create a table of areas; describe the pattern; explain why sliding the top vertex parallel to the base leaves area unchanged; and discuss how repeated area measurements can support practical land and water-management decisions. Treat the context as a mathematical model and distinguish measured environmental data from assumptions.