Respuesta :

To answer this you will draw a trapezoid and label the points A through D in order. See the picture I have attached. When you create triangle ACD, you have the base of the triangle as 10 and you know the total area. Using this information you can find the height. See the work in the picture. You will solve the equation to find the Height. When you know the height, then you can use the formula for area the trapezoid to find the area of this trapezoid. I have included the work for all the steps described.
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To find the area of the trapezoid we need to find the height of the trapezoid.

Trapezoid

A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.

Area of Trapezoid

The area of a trapezoid is given as half of the product of the height(altitude) of the trapezoid and the sum of the length of the parallel sides.

[tex]\rm{ Area\ of\ trapezoid = \dfrac{1}{2}\times \ height \times (Sum\ of\ the\ parallel\ Sides )[/tex]

The area of the trapezoid is 54 units².

Given to us

  • ABCD is a trapezoid,
  • AD = 10, BC = 8,
  • CK is the altitude altitude
  • Area of ∆ACD = 30

Area of  ∆ACD,

In ∆ACD,

[tex]\rm { Area\ \triangle ACD = \dfrac{1}{2}\times base\times height\\\\ [/tex]
Substituting the values,

[tex]30 = \dfrac{1}{2}\times AD\times CK\\\\ 30 = \dfrac{1}{2} \times 10 \times CK\\\\ \dfrac{30\times 2}{10} = CK\\\\ CK = 6\ units[/tex]

Area of Trapezoid ABCD

[tex]\rm{ Area\ of\ trapezoid = \dfrac{1}{2}\times \ height \times (Sum\ of\ the\ parallel\ Sides )[/tex]

[tex]Area\ ABCD= \dfrac{1}{2}\times \ CK \times (AD+BC )[/tex]

[tex]Area\ ABCD= \dfrac{1}{2}\times \ 6 \times (10+8 )\\\\ Area\ ABCD= \dfrac{1}{2}\times \ 6\times (18 )\\\\ Area\ ABCD= 54\ units^2[/tex]

Hence, the area of the trapezoid is 54 units².

Learn more about Trapezoid:

https://brainly.com/question/4758162

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