Question

Let ABCD be a trapezoid such that side [AB] and side [CD] are perpendicular to side [BC]. Let E be a point on side [BC] such that AED is equilateral. If |AB| = 7 and |CDI = 5, the area of trapezoid ABCD = m✓3 then m = ? ​

Answer 1

Answer:

Let ABCD be a trapezoid such that side [AB] and side [CD] are perpendicular to side [BC]. Let E be a point on side [BC] such that AED is equilateral. If |AB| = 7 and |CDI = 5, the area of trapezoid ABCD = m✓3 then m = ?

Answer 2

Concept

A quadrilateral with at least one pair of parallel sides s called trapezoid/. The number of vertices and edges in a trapezoid is 4. It has the properties like convex polygon.

Given

AB and CD are perpendicular to side BC. AED is an equilateral triangle. AB=7 and CD=5. The are of trapezoid is equal to m$\sqrt{3}$.

To find

Value of m.

Explanation

we have been give that ABCD is a trapezoid and AED is equilateral triangle. Draw a straight line from point C on AB which is perpendicular on AB and let the point on AB where the perpendicular meets AB is E.

In this way AE=5.

Let the side AD=x in such a way that EC=x.

Quadrilateral AECD is a rectangle as length and breadth of opposite sides are equal to each other.

Area of AECD=5*x

=5x

Area of triangle BEC=1/2*2*x

=x

Area of trapezoid ABCD=5x+x

=6x

Area is given as m$\sqrt{3}$

6x=m$\sqrt{3}$

2$\sqrt{3} \sqrt{3}$x=m$\sqrt{3}$

By comparing both sides we can say that the value of m will be 2$\sqrt{3}$*side of triangle AED.

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