Sign up to access problem solutions.

Already have an account? Log in here.

These shapes have four sides and 360° of interior angle goodness.

Suppose \(ABCD\) is an isosceles trapezoid with bases \(AB\) and \(CD\) and sides \(AD\) and \(BC\) such that \(|CD| \gt |AB|.\) Also suppose that \(|CD| = |AC|\) and that the altitude of the trapezoid is equal to \(|AB|.\)

If \(\dfrac{|AB|}{|CD|} = \dfrac{a}{b},\) where \(a\) and \(b\) are positive coprime integers, then find \(\large a^{b}.\)

Sign up to access problem solutions.

Already have an account? Log in here.

The numbers \(3,4,\) and \(6\) denote the area enclosed by their respective triangles.

What is the area of the yellow region?

Sign up to access problem solutions.

Already have an account? Log in here.

On square \(ABCD\), points \(E,F,G\), and \(H\) lie on sides \(\overline{AB},\overline{BC},\overline{CD},\) and \(\overline{DA},\) respectively, so that \(\overline{EG} \perp \overline{FH}\) and \(EG=FH = 34\). Segments \(\overline{EG}\) and \(\overline{FH}\) intersect at a point \(P\), and the areas of the quadrilaterals \(AEPH, BFPE, CGPF,\) and \(DHPG\) are in the ratio \(269:275:405:411.\) Find the area of square \(ABCD\).

Sign up to access problem solutions.

Already have an account? Log in here.

I want to make a litter box for my newly adopted pet kitten Admiral. The box is a cuboid with the top removed. I want the volume of the box to be 32 but the surface area to be minimized.

What is the minimum internal surface area I can achieve?

Sign up to access problem solutions.

Already have an account? Log in here.

\( ABCD \) is a parallelogram. Point \(P\) on \(AB\) divides it in the ratio \( AP : PB = 3 : 2 \), and point \(Q\) on \(CD\) divides it in the ratio \( CQ : QD = 7 : 3 \). Let \(R\) be the intersection of \( PQ \) and \(AC\). Then, \( AR : AC = a : b \), where \(a\) and \(b\) are positive coprime integers. What is \(a + b \)?

Sign up to access problem solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...