Area of trapezoids

Learning Objectives Recall and correctly apply the formula for the area of a trapezoid. Derive the formula for the area of a trapezoid by decomposing the shape into triangles and a rectangle. Calculate the area of a trapezoid given the lengths of its bases and its perpendicular height. Algebraically manipulate the area formula to solve for a missing dimension (base or height) given the area. Apply the area of a trapezoid formula to solve problems involving composite figures. Use trigonometric ratios to determine the height of a trapezoid when an interior angle and leg length are provided. Ever wondered how architects design sloped roofs or how surveyors measure irregularly shaped land? 🏞️ Many of these real-world shapes are trapezoids! This tutorial will review the fundamen...

TermDefinitionExample TrapezoidA quadrilateral with exactly one pair of parallel sides.A four-sided figure where the top side is parallel to the bottom side, but the left and right sides are not parallel to each other. Bases (b₁ and b₂)The two parallel sides of a trapezoid. They are often referred to as the 'top base' and 'bottom base'.In a trapezoid with a horizontal top and bottom, these are the horizontal sides. LegsThe two non-parallel sides of a trapezoid.The slanted sides that connect the ends of the two bases. Height (h)The perpendicular distance between the two bases. It is crucial that this is a perpendicular measurement, not the length of a slanted leg.A line segment drawn from one base to the other that forms a 90° angle with both bases. Isosceles TrapezoidA...

Area of a Trapezoid Formula A = \frac{1}{2}(b_1 + b_2)h This is the primary formula for finding the area (A) of a trapezoid. To use it, you must know the lengths of the two parallel bases (b₁ and b₂) and the perpendicular height (h). Area of a Trapezoid using the Median A = m \cdot h \quad \text{where} \quad m = \frac{b_1 + b_2}{2} This is an alternative form of the area formula. It is useful if you know the length of the median (m) and the height (h). It shows that the area of a trapezoid is equivalent to the area of a rectangle with a width equal to the trapezoid's median.