Use Perpendicular Height for Triangle and Parallelogram Area

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: A triangle has base 10 cm and perpendicular height 7 cm.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A parallelogram can be rearranged into a rectangle with the same base and perpendicular height. Its area is base times height. A triangle with the same base and height has half that area. The sloping side is not generally the perpendicular height, so using it changes the measured region.

Identify the stated base and perpendicular height. Use base × height for a parallelogram and half that product for a triangle. Explain the rectangle relationship and report square units. Do not substitute an unstated sloping-side length.

Check that the height is perpendicular to the base line. A triangle needs half the corresponding base-by-height rectangle area. Draw the base line and its right-angle height marker before computing area.

1. Draw the base line and its right-angle height marker before computing area.
2. Work through the supplied example and label what each number or attribute represents.
3. Identify the stated base and perpendicular height.
4. Answer the check, then try the three changed-input practice questions and explain one correction.

Check your reasoning

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Take it further

A triangle with base 13 and perpendicular height 4 has area 26 square units.

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