Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

Number of problems found: 2258

Compute 4
Compute the exact value of the triangle area with sides 14 mi, 12 mi, and 12 mi long.
Decide 2
Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line
Square sides
If we enlarge the side of the square by a third, its circumference will be 20 cm larger than the original. What is the side of the square?
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.
Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
Chord BC
A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
Tiles
The tile has the shape of a square with a side of 15 cm. What dimensions can a rectangle composed of 90 of these tiles have so that no tile remains?
Cardboard box
Peter had square cardboard. The length of the pages was an integer in decimetres. He cut four squares with a side of 3 dm from the corners and made a box out of it, which fit exactly 108 cubes with an edge 1 dm long. Julia cut four squares with a side of
Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
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
Five-gon
Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
Annulus
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
Coordinates of a centroind
Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
Two gardens
The total area of the two gardens is 864 m². The first garden is 60 m² smaller than three times the second garden. What is the area of each garden?
Negative and postcard
The image on the negative has dimensions of 36x24 mm and is enlarged to a postcard format of 13.5x9 cm. In what proportion have the lengths increased? In what proportion has the image content increased?
The length
The length of the circle is 24 cm. What is the length of the circular arc of the corresponding angle 30°?
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 the radius R = 6370 km
Tropics and polar zones
What percentage of the Earth's surface lies in the tropical, temperate, and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'.
Tetrahedral pyramid 8
Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p