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Home › Math & Conversions › Core Math & Algebra › Trapezoid Area Calculator Trapezoid Area Calculator This trapezoid area calculator lets you compute the area of a trapezoid in several ways: from bases and height , from bases and equal leg for an isosceles trapezoid, or directly from the coordinates of the four vertices . It also reports perimeter (when side lengths are known), the midsegment length , and the height (if it is derived instead of entered). Results are designed for both students and professionals who need fast and reliable geometric calculations. 1. Enter trapezoid dimensions Choose input method Bases + height Isosceles (bases + leg) 4 vertices (coordinates) Linear unit meters (m) centimeters (cm) millimeters (mm) inches (in) feet (ft) Decimal places Provide both parallel bases \( b_1 \) and \( b_2 \), the height \( h \), and optionally the non-parallel sides \( c \) and \( d \) for the perimeter. Base 1 \( b_1 \) Base 2 \( b_2 \) Height \( h \) Side \( c \) (optional) Side \( d \) (optional) For an isosceles trapezoid , the two non-parallel sides are equal. Provide the two bases and the leg length. The calculator derives the height using Pythagoras and then computes area and perimeter. Base 1 \( b_1 \) Base 2 \( b_2 \) Leg (equal side) \( l \) Enter the coordinates of the four vertices of the trapezoid in order around the shape (clockwise or counterclockwise). The tool uses the shoelace formula to compute area and also returns side lengths. Vertex A Vertex B Vertex C Vertex D Calculate Clear All dimensions must use the same linear unit 2. Results Geometric summary Method: Key inputs: Classification: Area & core metrics Area: Height: Midsegment length: Perimeter: Side lengths (when available) Formula used Trapezoid area – main formulas A trapezoid (or trapezium in some regions) is a quadrilateral with at least one pair of parallel sides. Those parallel sides are called the bases , usually denoted \( b_1 \) and \( b_2 \). The distance between them is the height \( h \). The fundamental area formula is \[ A = \frac{(b_1 + b_2)\,h}{2}. \] Intuitively, this is the area of a rectangle with height \( h \) and base equal to the average of the two bases: \[ A = \overline{m}\,h, \quad \overline{m} = \frac{b_1 + b_2}{2}. \] Isosceles trapezoid – bases and equal leg In an isosceles trapezoid the non-parallel sides (legs) are equal: \( c = d = l \). If we know the two bases \( b_1 \leq b_2 \) and the leg \( l \), we can recover the height using Pythagoras. The horizontal offset at each side is \[ x = \frac{b_2 - b_1}{2}, \] and the height is obtained from the right triangle: \[ h = \sqrt{l^2 - x^2}, \] assuming \( l \geq x \). Then the area follows from the main formula above. The perimeter is \[ P = b_1 + b_2 + 2l. \] Coordinates method – shoelace formula If the vertices \( A(x_1,y_1), B(x_2,y_2), C(x_3,y_3), D(x_4,y_4) \) are known in order around the trapezoid, we can compute the area using the shoelace formula : \[ A = \frac{1}{2}\left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1) \right|. \] The calculator also computes each side length using the Euclidean distance \[ \text{side length} = \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}, \] and reports the perimeter whenever all four sides are well-defined. Worked example – bases and height Suppose a trapezoid has bases \( b_1 = 8\;\text{m} \), \( b_2 = 14\;\text{m} \), and height \( h = 5\;\text{m} \). Compute the midsegment: \( \overline{m} = (8 + 14)/2 = 11 \;\text{m} \). Compute the area: \( A = \overline{m}\,h = 11 \cdot 5 = 55\;\text{m}^2 \). Entering these values into the calculator with unit meters returns an area of \( 55\;\text{m}^2 \), plus the chosen extra metrics if side lengths are supplied. Trapezoid geometry – FAQ What is the midsegment of a trapezoid? + The midsegment (or median) of a trapezoid is the segment that joins the midpoints of the two non-parallel sides. Its length is the average of the bases: \[ \overline{m} = \frac{b_1 + b_2}{2}. \] The area can be interpreted as the midsegment length times the height: \( A = \overline{m}\,h \). Do the non-parallel sides affect the area? + No. For a given pair of bases and height, the area is completely determined by \[ A = \frac{(b_1 + b_2)\,h}{2}. \] The non-parallel sides affect the perimeter and the overall shape but not the area, as long as the bases and the height remain fixed. How can I tell if four points form a trapezoid? + In analytic geometry, a quadrilateral is a trapezoid if at least one pair of opposite sides is parallel. You can check this by comparing slopes of sides: \[ \text{slope}(AB) = \text{slope}(CD) \] or \[ \text{slope}(BC) = \text{slope}(DA). \] This calculator focuses on area and does not fully validate whether a four-point input is strictly a trapezoid, so it is good practice to check the geometry if this matters. Core Math & Algebra tools Monte Carlo Simulation Lottery Odds Dot Product Matrix Determinant Partial Fraction Decomposition Trapezoid Area – you are here Combination and Permutation Torus Volume Matrix Transpose Surface Area Modular Exponentiation Related geometry tools Triangle Area Rectangle Area Circle Area
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