📐 Area of Triangles and Parallelograms

What you’ll learn

1. The Shortcut You Already KnowRecall that a rectangle's area is base × height, and name the base and height as the two perpendicular sides.Area comes from multiplying two sides of a rectangle rather than counting squares. We name them base and height, and stress that they meet at a right angle — the idea the whole course builds on.
2. Meet the ParallelogramDefine a parallelogram as a shape with two pairs of parallel sides, and see it as a pushed-over rectangle.A parallelogram has opposite sides parallel and equal; a rectangle is a special parallelogram with square corners. Pushing a rectangle's top sideways makes a parallelogram, setting up the question of whether area changed.
3. The Cut-and-Slide TrickExplain why a parallelogram's area is base × height using the cut-and-slide rearrangement.Cutting a right-triangle wedge off one end of a parallelogram and sliding it to the other end forms a rectangle of the same base and height, without adding or removing area. Therefore area = base × height.
4. Which Line Is the Height?Identify the perpendicular height of a parallelogram and reject the slanted side.The height is the perpendicular distance between base and top edge, not the longer slanted side. Because area depends only on base and height, two parallelograms with the same base and height have equal areas regardless of lean.
5. A Triangle Is Half a ParallelogramDerive and apply the triangle area formula ½ × base × height.Two identical triangles form a parallelogram, so a triangle is half of base × height. Learners apply the two-step move: multiply base by height, then halve.
6. The Height Trap, AgainRecognize that a triangle's height is perpendicular (and can fall outside the shape), and that any side can serve as the base.A triangle's height is the perpendicular distance from a chosen base to the opposite vertex, sometimes landing outside the triangle. Any of the three sides may be the base, and ½ × base × height gives the same area.
7. Put It to WorkApply both area formulas to mixed shapes and real-world contexts.Learners compute parallelogram and triangle areas and connect them to real jobs like sailmaking and gardening, reinforcing the through-line that every straight-sided area comes back to base × height.

Questions this course answers

Grounded in trusted sources

• Britannica — Area (geometry); Parallelogram; Triangle
• Illustrative Mathematics — Grade 6, Unit 1: Area and Surface Area
• Common Core Math — 6.G.A.1 (area of triangles and parallelograms)

Every Wunder lesson is built from real, reputable sources — never invented.

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