📐 Shapes

Sides, angles, and how to find the area of each one.

⬛ Square (Kvadrat)

4 equal sides, 4 right angles (90° each). All squares are also rectangles!

Area = s × s = s²

s

▭ Rectangle (Rektangel)

4 right angles, opposite sides equal. Doesn't need all 4 sides the same length, just the ones across from each other.

Area = l × w

l w

🔺 Triangles (Trianglar)

Every triangle has 3 sides and 3 angles that always add up to 180°, no matter the shape. Triangles are grouped by their sides:

Equilateral (liksidig): all 3 sides (and angles) equal.
Isosceles (likbent): 2 sides (and angles) equal.
Scalene (oliksidig): no sides equal.
A right triangle (rätvinklig triangel) is a different kind of grouping — by angle instead of sides — any triangle with one 90° angle.

Equilateral Isosceles Scalene

The height is always measured straight up from the base (at a right angle to it), even when the triangle isn't a right triangle.

Area = ½ × b × h

b h

▱ Parallelogram (Parallellogram)

Opposite sides are parallel and equal length; opposite angles are equal too. A rhombus (romb) is a parallelogram where all 4 sides are equal.

Area = b × h  (same idea as a rectangle — base times height, even though it's slanted)

b h

⏢ Trapezoid (Trapets)

Only one pair of sides is parallel (the top and bottom here, a and b) — the other two sides can be any length.

Area = ½ × (a + b) × h  (average the two parallel sides, then multiply by the height)

a b h

⬠ Pentagon (Femhörning)

5 sides. In a regular pentagon (all sides and angles equal, like this one), every interior angle is 108° — all 5 add up to 540°.

108°

⬡ Hexagon (Sexhörning)

6 sides — honeycomb cells and stop-sign... wait, stop signs are octagons! Hexagons show up in honeycombs and snowflakes. A regular hexagon's interior angles are 120° each, adding up to 720°.

120°

🔢 The Pattern Behind Every Polygon's Angles

Notice the angle sums so far: triangle 180°, square/rectangle 360°, pentagon 540°, hexagon 720°. Each shape adds exactly 180° more than the one before it, because every extra side lets you fit one more triangle inside the shape. That gives a formula that works for any polygon with n sides:

Angle sum = (n − 2) × 180°

Try it on an octagon (åttahörning — 8 sides, like a stop sign): (8 − 2) × 180° = 1080° — and since a regular octagon splits that evenly across 8 equal angles, each one is 135°.

135°