Posted by Cathy on Saturday, December 1, 2012 at 7:16am.
In a cyclic quadrilateral, the diagonal would be the hypotenuse of two right-angled triangles.
Clearly if the hypotenuse , in this case the diagonal, is 4√3, then the two given sides of 4 and 5 cannot be sides of the same triangle.
I made the following sketch
Quad ABCD in a circle, with BD as the diagonal of 4√3
AB = 5 and BC = 4
in triangle ABD
AD^2 + 5^2 = (4√3)^2
AD^2 = 48-25 = 23
AD = √23
It should also be obvious that the other triangle BCD is congruent to the first one.
So total area = 2 (1/2)(5)(√23 = 5√23
Related Questions
solid mensuration - The base of a right prism is a rhombus whose sides are 20cm ...
geometry - The sides of a quadrilateral are 3, 4, 5, and 6. Find the length of ...
geometry - The sides of a quadrilateral are 3, 4, 5, and 6. Find the length of ...
Geometry - The sides of a quadrilateral are 3, 4, 5, and 6. What is the length ...
solid mensuration - Find the area of a segment of a circle whose diameter is 16 ...
Math - How many cubic units are in the volume of a cylinder whose height is four...
math - What is the fourth measure for a quadrilateral angle whose 3 sides equal ...
solid mensuration - what is the area of a section bounded by a closed elliptical...
Geometry PLEASE HELP ME - What is the range of possible values for x? The ...
GEOMETRY - ABCD is a cyclic trapezium whose sides AD and BC are parallel to each...
For Further Reading
