Grade 8 Pythagoras: Find a Missing Side Worksheets
The hypotenuse and one shorter side are given — subtract before you take the root.
Every sheet below is generated fresh with a matching answer key. Pick one of the three levels, preview it, and print or download the PDF — no account, no watermark. For the other grade 8 geometry skills, see all geometry worksheets.
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Geometry · Grade 8
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Grade 8 · 3 pages · A4What each level generates
Grade 8 pythagoras: find a missing side — the exact skill behind each difficulty setting, straight from the generator.
- Level 1The hypotenuse and one side
- Level 2Larger triangles to work back through
- Level 3Ladders, fields and masts
Grade levels follow the progression common to most English-language curricula — not one specific national curriculum. Every level shows exactly what it generates, so you can check the fit with your own program. See the full scope & sequence →
More Grade 8 geometry skills
Each one generates a different kind of question, with its own three levels and answer key.
- Square Roots and Cube RootsFind the number that was squared or cubed, then combine two roots in one question.
- Pythagoras: Find the HypotenuseBoth shorter sides are given — square them, add, and find the square root.
- Distance Between Two PointsCount two sides off a grid, in one quadrant or all four, and find the slanting line between the points.
Frequently asked questions
▸What is the Pythagorean theorem?
In a right-angled triangle, the two shorter sides squared and added give the longest side squared: a² + b² = c². The longest side, opposite the right angle, is called the hypotenuse. Find the Hypotenuse practises the rule going forwards, and Find a Missing Side runs it backwards as a subtraction.
▸Are the answers always whole numbers?
Yes. Every triangle on these sheets is built from a Pythagorean triple — 3-4-5, 5-12-13, 8-15-17, 7-24-25, 20-21-29, 9-40-41 or a multiple of one — so every hypotenuse and every missing side is an exact whole number. Nothing is rounded, which means a wrong answer always points to a wrong method rather than to a decimal that slipped.
▸How do you find the distance between two points?
Subtract the two x values for the horizontal gap and the two y values for the vertical gap, ignoring any minus signs, then treat those as the shorter sides of a right-angled triangle. From (1, 5) to (5, 8) the gaps are 4 and 3, so the distance is 5 units. Distance Between Two Points draws the grid on two of its three levels, so the gaps are counted off the picture rather than read out of the sentence, and it builds up to a pair placed in opposite quadrants.
▸Why is there no Grade 7 geometry page?
Because there is nothing honest to put on it. Circles are the usual Grade 7 topic and they already have two sheets on the Grade 6 page, where the UK curriculum allows them; the rest of Grade 7 geometry is scale drawings and cross-sections, which need a diagram a length is measured off with a ruler. These sheets do print pictures — coordinate grids, plans of rectangles and triangles, circles, a cuboid, Grade 4's symmetry patterns and the angle cards at Grades 4 to 6 — but every one of them is read by counting, by looking, or off a number already written on the drawing, never by measuring, and a scale drawing is the opposite of that. An empty year is more useful than a padded one — print the Grade 6 circle sheets in Year 7 and come back here.
▸Do these worksheets need a diagram or a calculator?
No calculator — the numbers are chosen so the squaring and the roots can be done on paper. A diagram is printed where the question is about one: Distance Between Two Points draws the grid on two of its three levels, and the gaps are counted off it rather than read out of the sentence. The Pythagoras sheets draw the right-angled triangle on their first level, with the two sides you are given marked on it and the side you are asked for left blank; their second and third levels are written in words, because the triangles that level 2 works with are too large to print to scale. Tick the answer key box and the answers print on their own page at the end.