Area + goniometry and trigonometry - practice problems - page 4 of 8
Number of problems found: 149
- The bases
The bases of the isosceles trapezoid ABCD have 10 cm and 6 cm lengths. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and area of the ABCD trapezoid. - What percentage
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km. - Quadrilateral prism
Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - A drone
A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was 300 m above ABC's plane. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in meters. - Cone side
Calculate the volume and area of the cone whose height is 10 cm, and the axial section of the cone has an angle of 30 degrees between height and the cone side. - Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the base plane is α = 60°. - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - Circular railway
The railway connects in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track be from A to C? - Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³. - Calculate 9701
In the triangle, the side length AB = 6 cm, the height per side c = 5 cm, and the angle BCA = 35°. Calculate sides a b. - Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism? - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Isosceles 7661
The area of the isosceles triangle is 8 cm2, and its arm's length is 4 cm. Calculate the sizes of its interior angles. - Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface? - Diagonals of the rhombus
How long are the diagonals e, and f in the diamond if its side is 5 cm long and its area is 20 cm²? - Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm. - Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m - Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm - Tropical, mild and arctic
How many percent of the Earth's surface lies in the tropical, mild, and arctic ranges? The border between the ranges is the parallel 23°27' and 66°33'. - Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
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