# Area of shape - high school - math problems

#### Number of problems found: 237

- Ratio of squares

A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares? - Pentadecagon

Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places. - Hexagonal pyramid

Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm. - Half of halves

Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part? - The tent

Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m. - Hexagonal pyramid

Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm. - The funnel

The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel. - Which

Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm^{2}(B) 20 cm^{2}(C) 30.78 cm^{2}(D) 31.84 cm^{2}(E) 32.90 cm^{2} - Compute 4

Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long. - Regular hexagonal prism

Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long. - Triangular prism - regular

The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism. - Horses playground

The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m^{2}, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows? - Coordinates

Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0 - Hexagon

Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm. - Triangular prism,

The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm^{3}(l). - Triangular prism

The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism. - An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - 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´. - Eq triangle minus arcs

In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts - Quadrilateral pyramid

In a regular quadrilateral pyramid, the side edge is e = 7 dm and the diagonal of the base is 50 cm. Calculate the pyramid shell area.

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