Area of Triangles

Area of Triangles: Level 3 Challenges


Triangle ABC ABC has coodinates A=(4,0)A= (-4, 0), B=(4,0)B= (4 , 0), and C=(0,3)C= (0 , 3).

Let PP be the point in the first quadrant such that ABP\triangle ABP has half the area of ABC\triangle ABC but both triangles have the same perimeter.

What is the length of CP?CP? If your solution is in a form of d\sqrt{d}, submit dd as the answer.

Let ABCDABCD be a square of side length 12.

  • EE is the midpoint of CBCB,
  • FC=13DC FC = \frac{1}{3} DC ,
  • GD=14DA GD = \frac{1}{4} DA ,
  • AH=13AE AH = \frac{1}{3} AE ,
  • JJ is the midpoint of FEFE.

What is the area of the purple triangle?

Which of the following triangles has a larger area:

  • triangle A with side lengths 13,13,10 13, 13, 10 , or
  • triangle B with side lengths 13,13,24? 13, 13, 24\, ?

In the figure above triangle ABCABC with side-lengths AC=14AC=14, AB=13AB=13 and BC=15.BC=15. The incircle is drawn, which is tangential to all three sides. If the green shaded region is equal to AA, find A\left\lfloor A\right\rfloor .

What is the largest possible area of an isosceles triangle with two sides of length 2?


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