Four congruent equilateral triangles are placed in a row. A line connects the bottom left vertex of the first triangle to the top vertex of the last triangle. If each equilateral triangle has an area equal to 6, what is the area above the line contained within the triangles, as shaded in yellow?
A square with side length 1 is divided into 4 congruent right triangles, as shown, and a square in the center. Inscribe a circle in each triangle and in the center square. If all 5 circles are congruent, what is the radius of each circle?
Five congruent circles are placed with their centers equally spaced and collinear as shown. A line connects the bottom of the first circle and the top of the fifth circle. The area under the line enclosed by the circles, shown in yellow, is equal to 40. The overlapping area between two circles is 5. What is the area of a single circle?
Four right triangles with distinct integer hypotenuses are put together to form a quadrilateral, as shown in image. What's the smallest possible perimeter of this quadrilateral?
Note: Legs of the triangles need not to be integers.
Two triangles have integral side lengths, with all sides being less than 50. They are similar but not congruent and smaller triangle has two side lengths identical with the larger triangle.
What is the sum of the side lengths of the larger triangle?
