lesson
Perpendicular height is not a sloping side
1 · Learn
A parallelogram can be rearranged into a rectangle with the same base and perpendicular height, giving area = base × height. A triangle with the same base and height occupies half the area of a corresponding parallelogram.
The height meets the base line at a right angle. A sloping side is not automatically the height. Area uses square units; perimeter measures the boundary in length units.
2 · Worked example
A triangle with base 10 cm and perpendicular height 7 cm has area 35 cm². The matching parallelogram has area 70 cm².
3 · Your turn
Find the area of a triangle with base 12 cm and perpendicular height 5 cm, and a parallelogram with the same base and height.
Check your answer
30 cm² and 60 cm² respectively.
4 · Apply your learning
Cut and rearrange paper models with an adult, labelling the perpendicular height before measuring.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish fluency.
Open your writing and drawing pad
Write, draw or show your working. Use a mouse, pen or finger. This pad is not a submitted answer.
Not saved to your account. Download your drawing as PNG and your typed notes as TXT before leaving or refreshing. They are separate files. Do not enter private information.
Open a picture saved on this device to draw on it again. Opening replaces the drawing, but Undo can restore it. PNG only, up to 4 MB and 4096 × 4096 pixels. The picture stays in this browser; it is not uploaded. Paper lines in a saved picture become part of that picture.
Clear the drawing? Your typed notes will stay. You can undo this action.
Your pad is empty.
Open a UTF-8 TXT file from this device, up to 40 KB and 10,000 characters. It stays in this browser. Opening can be undone until you type again. Downloads keep a new copy; they do not change the file you opened.
Replace the notes on this page with the opened file? Download the current notes first if you want to keep them.
Typed notes are not submitted answers.
Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Practice this lesson
Lesson resources
Browse the available practice activities and worksheets for this lesson.
Your progress