Area of shape + Pythagorean theorem - math problems

Number of problems found: 225

The triangle
The triangle has sides 5 cm long, 5 cm, 8 cm long. What is the area of the triangle?
The quadrilateral
The quadrilateral ABCD is composed of two right triangles ABD and BCD. For side lengths: |AD| = 3cm, | BC | = 12cm, | BD | = 5cm. How many square centimeters (area) does the quadrilateral ABCD have? The angles DAB and DBC are right.
Equilateral triangle
Find the area of an equilateral triangle with a side of 15 cm.
Angle of diagonals
Calculate the perimeter and the area of a rectangle if its diagonal is 14 cm and the diagonals form an angle of 130°.
The diamond
The diamond has an area S = 120 cm², the ratio of the length of its diagonals is e: f = 5: 12. Find the lengths of the side and the height of this diamond.
A Cartesian framework
1. In a Cartesian framework, the functions f and g we know that: the function (f) is defined by f (x) = 2x ^ 2, the function (g) is defined by g (x) = x + 3, the point (O) is the origin of the reference, point (C) is the point of intersection of the graph
Side and diagonal
Find the circumference and the area of the rectangle if given: side a = 8 cm diagonal u = 10 cm.
Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?
Metal washers
Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet.
Outside point
The square ABCD and the point E lying outside the given square are given. What is the area of the square when the distance | AE | = 2, | DE | = 5 a | BE | = 4?
Truncated pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm.
Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.
Right isosceles triangle
What can be the area of a right isosceles triangle with a side length of 8 cm?
Ratio in trapezium
The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid
Ratio of triangles areas
In an equilateral triangle ABC, the point T is its centre of gravity, the point R is the image of the point T in axial symmetry, along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the area
Garden G
The rectangular, trapezoidal garden has a base length of 81m, 76m, and a vertical arm of 12m. Calculate how many m² of the area will remain for planting greenery if 1/3 of the area is built. Calculate the consumption of mesh for land fencing.
Right triangle
A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle?
Iglu - cone tent
The cone-shaped tent is 3 m high, the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m² of fabric is needed for production (including flooring), if 20% needs to be added to the minimum amount due to cutting waste? b
Vertex points
Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area.
Quadrilateral pyramid
Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture.