Maths Exam — Pythagoras Theorem, Perimeters and Formulae
Revise plane and solid geometry formulae: areas of triangles, squares, rectangles and circles; types of angles and triangles; the Pythagorean theorem with numerical examples; and volumes of cubes and cylinders — all explained after each question.
Geometry is the branch of mathematics that studies shapes, their measurements and their properties: points, lines, angles, polygons and solids in space. It is one of the most visual parts of maths and appears constantly in real life, from working out the area of a room to the volume of a tank.
In Primary and Secondary school the focus is on calculating perimeters, areas and volumes, the types of angles and triangles, and the Pythagorean theorem, which relates the sides of a right-angled triangle (a²+b²=c²). Mastering the basic formulas —area of a triangle, of a circle, volume of a cylinder— and knowing when to apply them is the key to the topic.
Revise all these formulas and concepts with the geometry exam below: 10 questions with an explanation after each answer, so you learn from mistakes and fix the procedures.
Mathematics · Primary, Secondary
Knowing that the triangle area is (base×height)/2 is not enough. The exam requires applying it with concrete numbers. Each explanation includes the full calculation.
a²+b²=c². The most common Pythagorean triples (3-4-5, 6-8-10) appear in the exam so students can automate them before tackling general cases.
Primary covers basic angles, triangle types, perimeters and simple areas. Secondary adds Pythagoras, cylinder and cube volumes, and circle areas.
"A Year 8 student always confused area with perimeter. After seeing the explanation "area in cm², perimeter in linear cm" across 3 questions, the confusion is gone."
Tricks and techniques to master this topic faster:
Angles: acute<90°, right=90°, obtuse between 90° and 180°, straight=180°. Interior angles of any triangle sum to 180°.
Triangle area = (base × height) / 2. Circle area = πr². Square area = L². Rectangle area = length × width.
Pythagoras only for right triangles: a²+b²=c² where c is the hypotenuse (longest side, opposite the right angle).
For volumes: cube = a³, cylinder = πr²×h. "Volume" always uses cubic units (cm³, m³).
If you are studying Geometry — Shapes, Areas and Volumes, these curriculum topics complement each other:
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