Right triangles
Areas of Regular Polygons
SOH-CAH-TOA
Geometric Probability
Surface Area
100
In a 30-60-90 triangle, the side opposite to the 30° is 6 yards Find the lengths of the longer leg and hypotenuse.
longer leg = 6 square root of 3
hypotenuse =12
100
Find the area of a pentagon that has radii of length 9. Round to the nearest tenth.
192.6
100
In a right triangle, one angle measures 25°, and the hypotenuse is 10 units. Find the length of the side opposite the angle, rounded to the nearest tenth.
4.2
100
What is the probability that a pebble dropped onto the board below lands on a blue circle? Round to the nearest tenth of a percent.
78.5%
100
A rectangular prism has a length of 5 cm, width of 3 cm, and height of 2 cm. What is its surface area?
62 square cm
200
This is the formula used to find the length of the missing side in a right triangle when two sides are known.
The Pythagorean theorem
200
Find the area of the figure. Round your answer to the nearest tenth.
90.8 mi2
200
In a right triangle, the angle is 67°, and the hypotenuse is 14 units. Find the adjacent side, rounded to the nearest tenth.
5.5
200
1/5
200
A cylinder has a radius of 4 cm and height of 10 cm. Find its total surface area.
351.68 cm2
300
In a 45-45-90 triangle, if each leg is 6 units long, this is the exact length of the hypotenuse.
6 square root of 2
300
Find the area of the hexagon. Round your answer to the nearest tenth.
221.7
300
A right triangle has an angle of 38° and an adjacent side of 9 units. Find the length of the opposite side, rounded to the nearest tenth.
7.0
300
Fly A:
1/2 > 1/4
300
A triangular prism has a height of 8 cm. The triangular base has a base of 6 cm and height of 4 cm, and the triangle's other two sides are each 5 cm. Find the surface area.
172 cm2
400
In a 30-60-90 triangle, the hypotenuse is 10 units. This is the exact length of the shorter leg and the longer leg.
shorter leg = 5
longer leg = 5 square root of 3
400
What is the area of the pentagon? Round your answer to the nearest tenth.
362.5
400
In a right triangle, the opposite side is 8.5 units, and the hypotenuse is 12 units. Use sine to find the measure of the angle, rounded to the nearest degree.
46°
400
A circular target has a radius of 10 cm. The bullseye is a smaller circle at the center with a radius of 2 cm. If an arrow hits the target at random, what is the probability it hits the bullseye? Express your answer as a decimal rounded to the nearest hundredth.
4%
400
A cone has a radius of 6 cm and a slant height of 10 cm. Find the surface area.
301.44 cm2
500
A right triangle has legs of length 7 and 24. This is the length of the hypotenuse.
25
500
The area of a regular heptagon is approximately 168 square units, and each side measures 5 units. Using this information, find the radius (distance from the center to a vertex), rounded to the nearest tenth.
10.7 units (or 9.9 using pythagoren theorem)
500
A ramp rises 3 feet vertically and makes an angle of 12° with the ground. Find the length of the ramp, rounded to the nearest tenth of a foot.
14.4 feet
500
A point is chosen at random inside a rectangle that is 10 units long and 8 units wide. Inside the rectangle is a circle centered in the middle with a radius of 4 units. What is the probability that the point lands inside the circle? Round your answer to the nearest hundredth.
50%
500
A solid is made of a cylinder with a hemisphere on top. The cylinder has a radius of 5 cm and height of 12 cm. Find the total surface area of the solid.
659.8 cm²