Area of Triangles

Area of Triangles - Problem Solving


If the lengths of the three sides of triangle ABC\triangle ABC sum to 13,13, and the inscribed circle has radius 8,8, what is the area of triangle ABC?\triangle ABC?

Consider a triangle inscribed in a circle with radius 2.2. If one side of the triangle is a diameter of the circle, what is the largest possible area of the triangle?

In the above diagram, we are given two side lengths AB=3,AC=9.\rvert \overline{AB} \lvert = 3, \rvert \overline{AC} \lvert = 9. If sin(B+C)=14,\sin(\angle B+ \angle C) = \frac{1}{4}, what is the area of ABC?\triangle ABC?

Note: The above diagram is not drawn to scale.

In the above right triangle, if ABC=30,ADC=45,BC=14,\angle ABC = 30^{\circ}, \angle ADC = 45^{\circ}, \lvert \overline{BC} \rvert = 14, what is the area of ADC?\triangle ADC?

Triangle ABCABC has vertices A=(4,k),A=(-4,k), B=(5,0)B=(5,0) and C=(4,6).C=(4,6). If the area of triangle ABCABC is 2323, what are the possible values of kk?


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