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PEAZIT Aha card

A trapezoid uses the average of its parallel sides

Two identical trapezoids form a parallelogram with base a + c. One trapezoid has half its area.

Parallel sides 8 and 4 cm; height 3 cm.

Relation	Meaning
S = (a + c) × h / 2	Add the parallel side lengths.
S = (8 + 4) × 3 / 2	Multiply by perpendicular height and halve.
S = 18 cm²	The result measures one trapezoid.

One worked example

S = (a + c) × h / 2Add the parallel side lengths.
S = (8 + 4) × 3 / 2Multiply by perpendicular height and halve.
S = 18 cm²The result measures one trapezoid.

Watch out: A sloping leg need not be the height. Height is the perpendicular distance between parallel sides.

Goal, prerequisites and card origin

What you will learn: Calculate area from parallel sides and height.

What you need first: Parallelograms and perpendicular lines.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

Show connections

Two identical trapezoids form a parallelogram with base a + c. One trapezoid has half its area.

Without JavaScript, write your answer elsewhere before opening the solution.Parallel sides are 10 and 4 cm and height is 5 cm. What is the area in cm²? Enter a number.

Solution — open after your own attempt

35 (10 + 4) × 5 / 2 = 35 cm².

A question for your next return: Parallel sides are 9 and 3 cm; height is 4 cm. What is the area in cm²?

Solution — open after your own attempt

24 (9 + 3) × 4 / 2 = 24 cm².

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