Engineering Board Exam Reviewer · Quadrilaterals · hard

A cyclic quadrilateral has sides 5, 6, 7, and 8. Using Brahmagupta's formula, find its area.

  1. 40.99
  2. 42.00
  3. 36.00
  4. 45.28

Answer

A. 40.99

Solution

s=5+6+7+8/2=13. Area =sqrt((13-5)(13-6)(13-7)(13-8))=sqrt(8(7)(6)(5))=sqrt(1680) 40.99.

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  1. An isosceles trapezoid has bases 10 and 24 and legs of length 13. Find its area.
  2. A rectangle has a perimeter of 34 and a diagonal of 13. Find its area.
  3. A rhombus has an area of 96 and one diagonal of 12. Find its perimeter.
  4. Two adjacent sides of a parallelogram are 8 and 12, and the angle between them is 30°. Find its area.
  5. Find the area of a trapezoid with parallel sides 8 and 14 and a height of 6.
  6. The diagonals of a rhombus are 10 and 24. Find the length of its side.
  7. Find the diagonal of a square whose side is 10.
  8. Find the area of a rectangle that is 12 units long and 7 units wide.
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