×
Back to all chapters

Composite Figures

Overlap, inscribe, and circumscribe a collection of simple geometric shapes to make a complex, composite figure.

Composite Figures: Level 3 Challenges

The side of the square is $$a$$. Express the green area with $$a$$.

Each square's vertex is a circumcentre of appropriate circular arc.

All the green triangles above are equilateral triangles.

What is the area of the triangle labelled as $$A$$ $$\big($$in $$\text{cm}^2\big)?$$

7 non-overlapping unit circles are inscribed inside a large circle as shown below. What is the area of the shaded region?

What is the area of the region enclosed by the graph of $$x^2+y^2=|x|+|y|$$?

 Notation: $$| \cdot |$$ denotes the absolute value function.

A rectangle is divided by four lines, as shown, with 4 of the resulting triangles having known areas. Find the area of the quadrilateral that is shaded in pink.

×