Answer:
Area of Quadrilateral = 289.57 sq.cm
Step-by-step explanation:
First of all, let us understand what is a Quadrilateral?
A quadrilateral is a polygon with four sides. A quadrilateral is a closed two-dimensional figure formed by joining the four points among which three points are non-collinear points.
Given,
Length of sides :
AB = 7.5 cm
BC = 11.7 cm
CD = 15.6 cm
AD = 18 cm
and given , the Angle between BCD is 90 degrees and the angle between BAD is 90 degrees.
It implies that the TRAINGLES BCD and BAD are Right angled triangles
So, the length of BD can be found using Pythagorean theorem
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
From the Triangle of BCD,
a= BC
b=CD and
c= BD
Therefore, The length of BD =
c=
c =
c = 19.5 cm
Hence, c= BD=19.5 cm
Now, Area of Quadrilateral =
1/2*(diagonal)*(sum of height of two triangles)
Here, Diagonal = Length of BD = 19.5 cm
Height (h1) = BC = 11.7 cm
Height ( h2) = AD = 18 cm
Therefore, Area = 1/2*19.5*(11.7+18)
= 289.57 sq.cm
Refer more about Area at below link:
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The value of x is 15.56.
Solution:
Tangent and Secant theorem:
If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.
BE = 22 BD = x, CD = x
BC = x + x = 2x
By the tangent and secant theorem,
Divide by 2 on both sides of the equation, we get
Take square root on both side of the equation.
x = 15.56
Hence the value of x is 15.56.