Step-by-step: area of trapezium and rhombus

Here is a clear, step-by-step guide to calculating the area of a trapezium and a rhombus.

Area of a Trapezium

A trapezium is a quadrilateral with one pair of parallel sides.

Formula:Area = (1/2) × (a + b) × h

• a and b are the lengths of the two parallel sides.
• h is the perpendicular distance (height) between the parallel sides.

Step-by-Step Guide:

1. Identify the parallel sides: Find the two sides of the trapezium that run parallel to each other. Let their lengths be 'a' and 'b'.
2. Identify the height: Find the perpendicular distance between these two parallel sides. This is 'h'.
3. Sum the parallel sides: Add the lengths of 'a' and 'b' together: (a + b).
4. Multiply by the height: Take the sum from Step 3 and multiply it by the height 'h': (a + b) × h.
5. Divide by 2: Divide the result from Step 4 by 2 to get the final area.

Area of a Rhombus

A rhombus is a quadrilateral with all four sides equal. Its diagonals bisect each other at right angles.

Formula:Area = (1/2) × d1 × d2

• d1 is the length of the first diagonal.
• d2 is the length of the second diagonal.

Step-by-Step Guide:

1. Identify the diagonals: Find the lengths of the two diagonals of the rhombus (the lines connecting opposite corners). Let them be 'd₁' and 'd₂'.
2. Multiply the diagonals: Multiply the lengths of the two diagonals together: d1 × d2.
3. Divide by 2: Divide the result from Step 2 by 2 to find the area of the rhombus.