Wednesday

April 16, 2014

April 16, 2014

Posted by **Cathy** on Saturday, December 1, 2012 at 7:16am.

Please include solution. Thanks.

- solid mensuration -
**Reiny**, Saturday, December 1, 2012 at 9:19amIn 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 ...

solid mensuration - Find the area of a segment of a circle whose diameter is 16 ...

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 ...

solid mensuration - what is the area of a section bounded by a closed elliptical...

solid mensuration - What is the area of a section bounded by a closed elliptical...

Geometry - The sides of a quadrilateral are 3, 4, 5, and 6. What is the length ...

solid mensuration - find the area of a regular pentagram if one of the sides of ...

math - 1. find the lateral area of a right prism whose altitude measures 20 cm ...

solid mensuration - Find the area of a portion of a semicircle of radius 15 m ...