Area of shape + expression of a variable from the formula - math problems
- 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.
- 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.
- Squares ratio
The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
- 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 cm3 (l).
- Free space in the garden
The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large
- Hexagonal pyramid
Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
- 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.
- The quadrilateral pyramid
The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
- Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
- Two bodies
The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco
- Cross five
The figure on the picture is composed of the same squares and has a content of 45cm². What's its perimeter?
- Diagonal intersect
isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles?
- Perimeter of the circle
Calculate the perimeter of the circle in dm, whose radius equals the side of the square containing 0.49 dm2?
- Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base 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´.
- Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
- The schoolyard
The schoolyard had the shape of a square with an 11m side. The yard has been enlarged by 75 m2 and has a square shape again. How many meters was each side of the yard enlarged?
- Two patches
Peter taped the wound with two rectangular patches (one over the other to form the letter X). The area sealed with both patches at the same time had a content of 40cm2 and a circumference of 30cm. One of the patches was 8cm wide. What was the width of t
- The parabolic segment
The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment a) around its base b) around its axis.
- Rectangle field
The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?