Area of Triangles: Level 3 Challenges Practice Problems Online

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

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

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

Let $ABCD$ be a square of side length 12.

$E$ is the midpoint of $CB$ ,
$FC = \frac{1}{3} DC$ ,
$GD = \frac{1}{4} DA$ ,
$AH = \frac{1}{3} AE$ ,
$J$ is the midpoint of $FE$ .

What is the area of the purple triangle?

Which of the following triangles has a larger area:

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

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

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

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Area of Triangles: Level 3 Challenges