Area + goniometry and trigonometry - practice problems - page 7 of 8
Number of problems found: 153
- Regular quadrangular pyramid
How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge of 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%. - Goat
Meadow is a circle with a radius r = 19 m. How long must a rope tie a goat to the pin on the Meadow's perimeter to allow the goat to eat half of the Meadow? - Goat and circles
What is the radius of a circle centered on the other circle, and is the intersection of the two circles equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which - Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
- De Moivre's formula
There are two distinct complex numbers, such that z³ is equal to 1 and z is not equal to 1. Calculate the sum of these two numbers. - ISO trapezium
Calculate the area of an isosceles trapezoid with base 95 long, leg 27 long, and with the angle between the base and leg 70 degrees. - House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How much m² is needed to cover the roof if the roof pitch is 57° and we calculate 11% of waste, connections, and overlapping of area roof? - Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c has dimensions in the ratio of 7:8:10. If you know that the diagonal wall AC is 56 cm, and the angle between AC and space diagonal AG is 25 degrees. - Hexagon A
Calculate the area of a regular hexagon inscribed in a circle with radius r=9 cm.
- Isosceles trapezoid
Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid. - Geodesist
Triangle-shaped field (triangle ABC) has a side AB = 129 m. path XY is parallel to the side AB, which divides triangle ABC into two parts with the same area. What will be the length of path XY? Help, please, geodesist. - Rotary cone
The volume of the rotation of the cone is 472 cm³. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Tower
How many m² of the copper plate should be replaced on the roof of the conical tower shape with a diameter 23 m, and the angle at the axial section's vertex is 119°? - Cone
Calculate the volume and surface area of the cone with a diameter of the base d=15 cm and the side of the cone with the base has angle 52°.
- Diagonal
The diagonal of the rectangle has a length of 41.4 cm. The angle between the diagonal and longer side of the rectangle is 26°. Calculate the area of the rectangle. - Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles. - Triangle
Calculate the area of the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius). - SAS triangle
The triangle has two sides, long 7 and 19, and makes included angle 110°42'. Calculate the area of this triangle. - Parallelogram
Calculate area of the parallelogram ABCD as shown if |AB| = 13 cm, |BC| = 99 cm and angle BAD = 100°
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