Answer:
25
Step-by-step explanation:
Using the Pythagorean Theorem, we can find the side length of each side.
a^2 + b^2 = c^2
=> 3^2 + 4^2 = x^2
=> 9 + 16 = x^2
=> x = 5
By applying the same formula for each side, we will get that each side is 5 units.
So, the area = 5*5 = 25
The quadrilateral is a square and the area of square is 25 square units.
A quadrilateral is 2-dimensional geometric closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.
For the given situation,
The quadrilateral ABCD has points A(0,4), B(3,0), C(7,3), D(4,7).
The distance these points can be found by
[tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
AB = [tex]d=\sqrt{(3-0)^{2}+(0-4)^{2} }[/tex]
⇒ [tex]AB = \sqrt{3^{2}+4^{2} }[/tex]
⇒ [tex]AB=\sqrt{9+16}[/tex]
⇒ [tex]AB=\sqrt{25}[/tex]
⇒ [tex]AB=5[/tex]
BC = [tex]d=\sqrt{(7-3)^{2}+(3-0)^{2} }[/tex]
⇒ [tex]BC=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]BC=5[/tex]
CD = [tex]d=\sqrt{(4-7)^{2}+(7-3)^{2} }[/tex]
⇒ [tex]CD=\sqrt{(-3)^{2} +4^{2} }[/tex]
⇒ [tex]CD=5[/tex]
DA = [tex]d=\sqrt{(4-0)^{2}+(7-4)^{2} }[/tex]
⇒ [tex]DA=\sqrt{4^{2}+3^{2} }[/tex]
⇒ [tex]DA=5[/tex]
Since AB = BC = CD = DA, the quadrilateral is a square.
The formula of area of quadrilateral is
[tex]A=(side)^{2}[/tex]
⇒ [tex]A=5^{2}[/tex]
⇒ [tex]A=25[/tex]
Hence we can conclude that the quadrilateral is a square and the area of square is 25 square units.
Learn more about quadrilaterals here
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