Trapezoids

Geometry · Axiom Academy

Quadrilaterals with exactly one pair of parallel sides Start with four vertices A , B , C , D . The top and bottom sides run in the same direction — they're parallel , and we call them the bases . The two slanted sides point in different directions — they're not parallel, and we call them the legs . 2. Bases, Legs, and the Height The height h is the perpendicular distance between the two bases — measured straight across, not along a slanted leg. Watch it drop in at a right angle. The two parallel sides. They can be different lengths. The two non-parallel sides connecting the bases. The perpendicular distance between the bases. Joins the leg midpoints; parallel to the bases. Two special trapezoids are worth knowing: One leg is perpendicular to both bases 3. Area: Average of the Bases × Height Slide the slanted corners inward until the trapezoid becomes a rectangle of the same height. Its width settles at the average of the two bases , and no area is gained or lost — so the trapezoid's area is that average width times the height. A trapezoid has bases of 8 cm and 14 cm, and a height of 6 cm. Find the area. Same-side angles: the two angles on a single leg sit between the parallel bases, so they are supplementary — they add to 180°. All four interior angles add to 360°, like any quadrilateral. You've named every part of a trapezoid, met the isosceles and right trapezoids, and seen why its area is the average of the bases times the height. Scroll up to revisit any step.

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