Quadrilaterals — Parallelograms, Trapezoids, Rectangles

ACT Math · Axiom Academy

Parallelograms, trapezoids, and rectangles — one family tree, three area formulas, and the perpendicular-height trap the ACT loves to set. 1. The Quadrilateral Family Tree Every shape here is a parallelogram with something added . Force the angles to 90° and a parallelogram becomes a rectangle ; make its sides equal too and it becomes a square . Equalize only the sides and you get a rhombus . A trapezoid is the outsider — just one pair of parallel sides. Watch the parallelogram specialize. 2. Parallelogram Area Is Base × Height Slice the triangle off one slanted end of a parallelogram and slide it to the other end. Nothing is added or removed — yet it becomes a plain rectangle with the same base b and the same perpendicular height h . So a parallelogram's area is exactly a rectangle's: A = bh . The slanted side never enters the area at all. base b × perpendicular height h — NOT the side length A = bh — base times perpendicular height. P = 2a + 2b — twice each pair of sides. Opposite sides are parallel and equal; opposite angles are equal. They are supplementary: . Diagonals bisect each other. Worked Example — Parallelogram A parallelogram has base 12 cm, height 8 cm, and a (non-base) side of 10 cm. Find the area and perimeter. 3. Trapezoid Area Is the Average Base × Height

This is the written version of the interactive lesson above. See the full ACT Math course.