Waste less time on Facebook — follow Brilliant.
×

Regular Polygons

With equal angles and equal side lengths, what more could you want from a polygon?

Triangular Decomposition - Polygons

         

Consider a rectangle with diagonals as shown in the above diagram. If the area of \(\triangle BCE\) is \(32,\) what is the area of \(\triangle ABE?\)

View solution
View wiki
by Brilliant Staff

The above diagram is a regular pentagram. Let \(\lvert\triangle TRS\rvert\) denote the area of \(\triangle TRS,\) and \(\lvert\square PQRS\rvert\) the area of \(\square PQRS.\) If \(\lvert\triangle ABC\rvert=52,\) what is the area of the shaded region \[\lvert\square PQRS\rvert - \lvert\triangle TRS\rvert?\]

View solution
View wiki
by Brilliant Staff

In the above diagram, \(\square ABCD\) is a square and \(\overline{DE}\) is perpendicular to one of its diagonals \(\overline{AC}.\) If the length of \(\overline{DE}\) is \(21.\) what is the length of \(\overline{AC}?\)

View solution
View wiki
by Brilliant Staff

In the above diagram, figure \(ABCDE\) is a regular pentagon centered at point \(F\). Find the area of quadrilateral \(CDEF\) when the area of triangle \(ABF\) is \(56.\)

View solution
View wiki
by Brilliant Staff

In \(\triangle ABC\) above, \(L,M\) and \(N\) are the midpoints of \(\overline {AB}, \overline {BC}\) and \(\overline {AC},\) respectively. If the area of \(\triangle LMN\) is \(54,\) what is the area of \(\triangle ABC?\)

View solution
View wiki
by Brilliant Staff
×

Problem Loading...

Note Loading...

Set Loading...