Geometry · Shape & Space
Name the measure, read the diagram, chain the rules.
1 Explore — try these first
Try before you watch. Pick a level below and give the problem an honest try on paper first — wrong turns and all. Then open the video to see the trick. Every level rides one habit: Name whether you want a LENGTH, an ANGLE, or an AREA, then use the shape’s property.
★ · Length, Angle, or Area?
A rectangle is 6 m long and 4 m wide. Three readers each ask a different question about the SAME rectangle: (a) the distance all the way around it, (b) the measure of one of its corners, (c) the space covered inside it. Give all three answers with units.
L0 · Perimeter Is the Boundary
A welcome path is built from 6 identical square mats joined edge-to-edge in a single row. Each mat is 1 m on a side. What is the perimeter of the whole path?
L1 · Fixed Perimeter → Half
A rectangular welcome garden has a perimeter of 30 m. The length is 3 m more than the width. What is the area of the garden?
L2 · Area = Base × Height
A rectangular help hall measures 8 m by 5 m. A triangular canopy sits on a base of 8 m with a height of 6 m. Find the area of the hall AND the area of the canopy.
L3 · Angles Combine
At the apex A of a canopy, a support ray AD splits the top angle ∠BAC into two parts. ∠BAD = 35° and ∠DAC = 28°. What is ∠BAC?
L4 · Exterior Angles Make 360
A regular polygon has each interior angle equal to 4 times its exterior angle at the same vertex. How many sides does the polygon have?
L5 · Similar Triangles
In triangle ABC, a sign band DE is drawn parallel to BC with D on AB and E on AC. AD = 4, DB = 6, and BC = 15. Find DE.
L6 · Chain the Angle Facts
On a circular pond with centre O, points A, B, C sit on the rim so OA = OB = OC are radii. The central angles are ∠AOB = 80° and ∠BOC = 40°. Find ∠ABC.
2 Learn — watch the solutions
Gave each one a real try? Now watch the trick. (Stuck is fine — that's the point.)
★ · What Are We Measuring?
Peek the trick — Name the Measure
Before you compute anything, decide whether the question wants a length (around the edge), an angle (the turn at a corner), or an area (the space inside). Naming the measure picks the unit and the rule.
L0 · Count the Outside Edges
Peek the trick — Count the Outside
Perimeter counts only the OUTSIDE edges of a shape. When identical tiles join in a row, every shared wall is hidden inside, so each new tile adds a fixed boundary amount — not its full edge count.
L1 · Half the Fence
Peek the trick — Half the Fence
For a rectangle, length + width is exactly half the perimeter. That single fact turns a perimeter clue into a clean sum you can split with any second hint.
L2 · Base × Height
Peek the trick — Base Times Height
A rectangle's area is base times height. A right triangle sitting on the same base with the same height is exactly half of that rectangle — same multiply, then halve.
L3 · Angles That Add Up
Peek the trick — Add or Subtract Angles
Angles that share a vertex ADD. A straight line is 180°, a full point is 360°, and a triangle's three angles also total 180° — so add or subtract to find the missing one.
L4 · The Polygon Angle Rule
Peek the trick — Polygon Angle Rule
Walk once around any polygon and your turns (exterior angles) total 360°. In a REGULAR polygon every turn is equal, so the number of sides is 360 ÷ (one exterior angle).
L5 · Parallel Makes Proportional
Peek the trick — Parallel Proportional
A line parallel to one side of a triangle cuts off a smaller triangle of the SAME shape. Every matching length scales by the same ratio — find that ratio once and apply it.
L6 · Angle Detective (capstone)
Peek the trick — Angle Detective
When no single fact closes a circle problem, CHAIN them. Equal radii make isosceles triangles, each triangle sums to 180°, and the angle at a rim point is built from those base angles.
3 Master — practice on your own
Print the practice sheet and solve without the videos. Check your answers at the back — if one is wrong, the answer key names the trick so you know exactly which video to rewatch.
Download fresh practice problems PDF
