Pathways, Trapezium & Rhombus Areas explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Some area problems use shapes that are not simple rectangles.
Pathways, trapeziums, and rhombuses need careful formula selection.
These ideas are useful in gardens, roads, floor designs, fields, and construction diagrams.
A trapezium has one pair of parallel sides. Its area depends on the two parallel sides and the height.
A rhombus has four equal sides. Its area can be found using its diagonals.
A pathway problem often has an outer area and an inner area. The path area is found by subtraction.
Always draw or read the diagram carefully before choosing a formula.
Meaning: A trapezium area uses the two parallel sides and height.
Definition: Area of trapeziu x sum of parallel sides x height.
If parallel sides are 8 cm and 12 cm, and height is 5 cm, are x 20 x c.
Meaning: A rhombus area can be found from its diagonals.
Definition: Area of rhombu x product of diagonals.
If diagonals are 10 cm and 12 cm, are x 10 x c.
Meaning: A pathway is a strip around or inside a shape.
Definition: Path area is usually found by subtracting inner area from outer area.
For a garden with a path around it, outer rectangle area minus inner garden area gives path area.
Meaning: Different shapes need different formulas.
Definition: Formula selection means matching the formula to the shape and given measurements.
Use trapezium formula when parallel sides and height are given. Use rhombus formula when diagonals are given.
Easy
Question: Find the area of a trapezium with parallel sides 6 cm and 10 cm, height 4 cm.
Medium
Question: Find the area of a rhombus with diagonals 9 cm and 14 cm.
Exam-level
Question: A rectangular garden is 20 m by 12 m. A path surrounds it, making the outer rectangle 24 m by 16 m. Find the path area.
Using slant side as height in a trapezium
Why it happens: The slant side is visible and labelled.
Correct approach: Height must be perpendicular to the parallel sides.
Forgetting the in formulas
Why it happens: Only multiplication is remembered.
Correct approach: Both trapezium and rhombus diagonal formulas include .
Adding inner and outer areas for pathways
Why it happens: Both areas are calculated correctly but combined wrongly.
Correct approach: Subtract inner area from outer area.
What are parallel sides in a trapezium?
They are the pair of opposite sides that never meet.
Are rhombus diagonals the same as sides?
No. Diagonals join opposite vertices. Sides form the boundary.
Why subtract in pathway problems?
The path is the part left after removing the inner area from the outer area.
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