Area of Trapezoid

Area of Trapezoid Definitions, Formula’s and Examples

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    How to find the Area of Trapezoids? – Formula, Examples, Derivation

    A trapezoid is a 2D geometric shape with four sides where two of the sides are parallel to each other. The area of a trapezoid can be calculated using the formula: A = 1/2 x (b1 + b2) x h, where b1 and b2 are the lengths of the parallel sides and h is the height. If you’re interested in learning how to find the area of a trapezoid, read on for a step-by-step guide, as well as several examples.

    What is a trapezoid?

    A trapezoid is a four-sided geometric shape with two parallel sides. The other two sides are not parallel and are referred to as the “legs” of the trapezoid. The legs of a trapezoid can be any length, but the two parallel sides must be of equal length.

    The formula for the area of a trapezoid

    A trapezoid is a four-sided geometric shape with two parallel sides. The other two sides are not parallel, and they come together at an angle. You can find the area of a trapezoid by using the formula:

    Area = 1/2 * (base1 + base2) * height

    To use the formula, you need to know the lengths of all four sides of the trapezoid. The bases are the two parallel sides, and the height is the distance between the bases.

    How to derive the formula for the area of a trapezoid

    A trapezoid is a four-sided figure with two sides that are parallel to each other. The formula for the area of a trapezoid is:

    Area = 1/2 * (Base1 + Base2) * Height

    To derive this formula, we can start with a rectangle. A rectangle has two parallel sides (the bases) and two non-parallel sides (the legs). If we cut off a triangle from one corner of the rectangle, we are left with a trapezoid.

    The area of the rectangle is: Area = Base * Height

    The area of the triangle is: Area = 1/2 * Base * Height

    Therefore, the area of the trapezoid is: Area = Rectangle Area – Triangle Area
    Area = Base * Height – 1/2 * Base * Height
    Area = 1/2 * Base * Height

    Examples of how to find the area of a trapezoid

    If you’re looking for examples of how to find the area of a trapezoid, you’ve come to the right place! In this article, we’ll show you step-by-step how to calculate the area of a trapezoid using the standard formula. We’ll also provide some tips and tricks for memorizing the formula, as well as some practice problems to help you better understand the concept.

    So what are you waiting for? Let’s get started!

    Surface Area of a Trapezoidal Prism

    A trapezoidal prism is a three-dimensional figure with two parallel sides, called bases, and four lateral faces that are trapezoids. The surface area of a trapezoidal prism is the sum of the areas of its lateral faces and its two bases.

    To find the surface area of a trapezoidal prism, we will use the formula:

    Surface Area = (2 * Base Area) + (4 * Lateral Face Area)

    Where:
    Base Area = (b1 + b2)/2 * h
    Lateral Face Area = l * h
    b1 and b2 are the lengths of the two bases and h is the height. l is the length of one side of a lateral face.

    Derivation of Surface Area of a Trapezoidal Prism

    Assuming that the trapezoidal prism shown in the figure is composed of two right trapezoids with bases b1 and b2 and heights h, we can find the total surface area of the prism by adding the areas of its six faces. The area of each rectangular side is simply bh, where b is a base and h is the height. There are two of these, so their combined area is 2bh. The area of each triangular end is 1/2b?, where b is a base and ? is the height; again, there are two of them for a total contribution of 2b?. Finally, the trapezoidal sides make a combined contribution of (b1+b2)h. Therefore, the total surface area A of the prism is
    A=2bh+2b?+(b_1+b_2)h=bh(2+b_1/b_2+1).

    Conclusion

    We hope that this article has helped you understand how to find the area of a trapezoid. If you have any questions, feel free to leave a comment below.

    Area of Trapezoid

    Result

    A = ((a + b) sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)))/(4 (b - a))

    Definition

    Defining inequalities

    y>=0 and y (a^2 - c^2 + d^2) + x sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) + b^2 y<=b (sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) + 2 a y) and sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) + 2 a y>=2 b y and x sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) + 2 a b y>=y (a^2 + b^2 + c^2 - d^2)

    Lamina properties

    (0, 0) | (b, 0) | ((a^2 - b^2 - c^2 + d^2)/(2 (a - b)), sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (-a + b))) | (-(a^2 - 2 a b + b^2 + c^2 - d^2)/(2 (a - b)), sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (-a + b)))

    4

    a>0 and b>0 and c>0 and d>0 and (a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)>0

    sqrt((a^2 (-b) + a b^2 - a c^2 + b d^2)/(b - a)) | sqrt((a^2 (-b) + a b^2 - a d^2 + b c^2)/(b - a))

    sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (b - a))

    x^_ = (b/2 + ((2 a + b) (c^2 - d^2))/(6 (-a^2 + b^2)), ((2 a + b) sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)))/(6 (-a^2 + b^2)))

    Mechanical properties

    J_x invisible comma x = -((3 a + b) ((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))^(3/2))/(96 (a - b)^3)

    J_y invisible comma y = -(sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) (a^5 - a^4 b + 6 a^3 b^2 - 6 a^2 b^3 - 8 a^2 b c^2 + 8 a^2 b d^2 - 7 a b^4 + 4 a b^2 c^2 - 4 a b^2 d^2 + 3 a c^4 - 6 a c^2 d^2 + 3 a d^4 + 7 b^5 + 4 b^3 c^2 - 4 b^3 d^2 + b c^4 - 2 b c^2 d^2 + b d^4))/(96 (a - b)^3)

    J_zz = (sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) (a^4 - 4 a^3 b - 3 a^2 (c^2 + d^2) + a b (6 c^2 - 2 d^2) + b^2 (3 b^2 + 3 c^2 - d^2)))/(48 (a - b)^2)

    J_x invisible comma y = ((a - b - c - d) (a - b + c - d) (a - b - c + d) (a - b + c + d) (2 b (2 a^2 + c^2) - (a + b) (2 b^2 + 3 c^2) + d^2 (3 a + b)))/(96 (a - b)^3)

    Distance properties

    b | d | a | c

    p = a + b + c + d

    max(b, sqrt((a^2 b - a b^2 + a d^2 - b c^2)/(a - b)), sqrt((a^2 b - a b^2 + a c^2 - b d^2)/(a - b)))

    χ = 1

    Expanded form

    (a sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)))/(4 (b - a)) + (b sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)))/(4 (b - a))

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