Polygons
In a triangle, one angle is three times as large as the smallest angle, and the third angle is 20° more than the smallest angle. Find the value of the largest angle.
96
A circular track has an inner diameter of 20 m and an outer diameter of 30 m. What is the area of the track? (Use pi)
125pi
A triangle has legs measuring x and 2x, and a hypotenuse of 10. Find x.
x = sqrt(2)
In a 30-60-90 triangle, the hypotenuse is 12. Find the shorter and longer legs.
6, 6*sqrt(3)
The diagonals of a rhombus are 12 cm and 16 cm. Find the perimeter of the rhombus.
40
A regular hexagon is inscribed in a circle with radius 8. What is the area outside the hexagon but inside the circle?
What is the area of an isosceles triangle with 22, 20, 22?
10sqrt(384) = 80sqrt(6)
A square is inscribed in a circle with radius r=10. Find the side length of the square.
10*sqrt(2)
A regular polygon has an interior angle of 162 degrees. How many sides does this polygon have?
20
Rudolph is tied to the bottom-left corner of a barn by a 10-foot-long rope. The barn is 18 feet wide and 10 feet long. How much area can Rudolph explore (he can't go in the barn)?
3/4 * 100pi = 75pi
A rectangle has a diagonal of 20 cm, and its sides are in a 3:4 ratio. Find the area of the rectangle.
192
In a 30-60-90 triangle, the area is 18*sqrt(3), and the longer leg is the height. Find the hypotenuse.
12