# 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: 1947

• Draw triangle
Construct an isosceles triangle ABC, if AB = 7cm, the size of the angle ABC is 47°, arms | AC | = | BC |. Measure the size of the BC side in mm.
• Trapezoid
How long are the trapezoid bases with area 24 cm2 and height 3 cm. One base is 3 times longer than the shorter.
• Rectangles
Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm?
• Flakes
A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
• 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?
• Slant height
The cone's slant height is 5cm, and the radius of its base is 3cm, find the volume of the cone.
• Body diagonal
Find the length of the body diagonal of a cuboid with lengths of 16 cm, 7 cm, and 4 cm.
• Jewel
Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
• Triangular prism
Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
• Combi-triangle
On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
• Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
• Diagonals of a rhombus 2
One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
• Interior angles
In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles.
• Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
• Medians in triangle
Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm.
• Hectares
Determine the area of the rectangular land (in ha), which has dimensions of 3 cm and 4.5 cm on the plan with a scale of 1: 40,000.
• Angle of two lines
There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
• Square and circles
The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.
• Garden
The rectangular garden has dimensions of 27 m and 30 m. Peter and Katka split it in a ratio of 4:5. How many square meters did Katkin measure part of the garden?