To recall, a trapezoid, likewise referred to as a trapezium, is a quadrilateral with one pair of parallel sides and also another pair that non-parallel sides. Choose square and rectangle, a trapezoid is likewise flat. Therefore, that is 2D.

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In a trapezoid, the parallel political parties are well-known as the bases, while the pair of non-parallel sides are known as the legs. The perpendicular distance in between the two parallel political parties of a trapezium is known as a trapezoid height.

In simple words, the base and height that a trapezoid are perpendicular to every other.

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122 = h2 + 62By Pythagorean theorem, the elevation (h) is calculated as;

144 = h2 + 36.

Subtract 36 ~ above both sides.

h2 = 108.

h = 10.39 cm.

Hence, the elevation of the trapezoid is 10.39 cm.

Now, calculation the area the the trapezoid.

Area that trapezoid = ½ h (b1 + b2) Sq. Units.

= ½ x 10.39 x (27 + 15) cm2.

= ½ x 10.39 x 42 cm2.

= 218.19 cm2.

Example 6

One base of a trapezium is 10 m more than the height. If the other base is 18 m and the trapezoid area is 480 m2, discover the height and also base of the trapezoid.

Solution

Let the height = x

Other basic is 10 m 보다 the height = x + 10.

Area that trapezoid = ½ h (b1 + b2) Sq. Units.

By substitution,

480 = ½ * x * (x + 10 + 18)

480 = ½ *x * (x + 28)

Use the distributive residential property to eliminate the parentheses.

480 = ½x2 + 14x

Multiply every term by 2.

960 = x2 + 28x

x2 + 28x – 960 = 0

Solve the quadratic equation come get;

x = – 48 or x = 20

Substitute the hopeful value of x in the equation of height and also base.

Height: x = 20 m.

The various other base = x + 10 = 10 + 20 = 30 m.

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Therefore, the other base and height the the trapezoid room 30 and 20 m, respectively.

Practice Problems

Find the area of a trapezoid, which has actually the parallel bases the lengths 9 units and also 12 units, and the elevation is 15 units.For a trapezoidal figure, the sum of the parallel bases is 25 m, and the elevation is 10 m. Recognize the area that this figure.Consider a trapezoid that area 112b square ft, whereby b is the much shorter base length. What is the height of this trapezoid if the lengths of two parallel bases room such that one basic is two times the other base?