Area of Triangles

Concept Quizzes

Area of Triangles Warmup
Triangles - Calculating Area
Area of Triangles - Sine Rule
Area of Triangles - Heron's Formula
Area of Triangles - Shoelace Formula
Area of Triangles - Problem Solving

Challenge Quizzes

Area of Triangles: Level 1 Challenges
Area of Triangles: Level 2 Challenges
Area of Triangles: Level 3 Challenges

Area of Triangles - Problem Solving

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

54 52 50 48

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by Brilliant Staff

Consider a triangle inscribed in a circle with radius $2.$ If one side of the triangle is a diameter of the circle, what is the largest possible area of the triangle?

2 4 6 8

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by Brilliant Staff

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

Note: The above diagram is not drawn to scale.

\frac{6}{1}

\frac{27}{10}

\frac{27}{8}

\frac{9}{2}

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by Brilliant Staff

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

\frac{65}{2}

\frac{14}{\sqrt{3}}

\frac{98}{3}

\frac{13}{\sqrt{3}}

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Triangle $ABC$ has vertices $A=(-4,k),$ $B=(5,0)$ and $C=(4,6).$ If the area of triangle $ABC$ is $23$ , what are the possible values of $k$ ?

8, 100

10, 100

10, 108

8, 108

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by Brilliant Staff