Speed< > to change
Math · 33 · Geometry and Trigonometry

Quadrilaterals

Notes

Key points

  • Interior angles sum to 360∘360^\circ.
  • Parallelogram: opposite sides equal, opposite angles equal, neighbours sum to 180°.
  • Parallelogram diagonals bisect each other.
  • Rectangle: equal diagonals. Rhombus: perpendicular diagonals. Square: both.
  • Trapezoid: exactly one pair of parallel sides (the bases).
  • Only the rectangle A=ℓwA=\ell w is on the reference sheet.

Formulas

RectangleA=ℓwP=2ℓ+2wA=\ell w\qquad P=2\ell+2w
ParallelogramA=bhA=bhh is the perpendicular height
TrapezoidA=12(b1+b2)hA=\dfrac{1}{2}(b_1+b_2)hNot on the reference sheet
Rhombus or kiteA=12d1d2A=\dfrac{1}{2}d_1d_2
SquareA=s2d=s2A=s^2\qquad d=s\sqrt{2}

Common traps

  • Using the slanted side as the height of a parallelogram or trapezoid.
  • Assuming a rectangle or square because it looks like one.
  • Composite perimeters: counting inside edges, or missing an outside edge.

SAT tip

Odd shapes: split into rectangles and right triangles, or subtract a cut-out from a bigger rectangle.

Test yourself

10 official SAT questions on Quadrilaterals, easiest first.

    Next lesson34 · Circles