# 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: 2136

• Four sides of trapezoid
Calculate the area of the ABCD trapezoid with sides a = 65 cm, b = 29 cm, c = 40 cm, d = 36 cm
• Company logo
The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
• Angles of the triangle
ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
• Squares
Calculate the area of square and result round to square decimeters. a) a = 1,52 dm b) a = 13 268mm c) a = 562 cm d) a = 1,52 m
The ladder touch on a wall at a height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall?
• A bug
A bug was sitting on the tip of a wind turbine blade that was 24 inches long when it started to rotate. The bug held on for 5 rotations before flying away. How far did the bug travel before it flew off? Exact answer.
• Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
• Roof angle
The roof of the house has the shape of an isosceles triangle with arms 4 m long and the size of the base 6 m. How big an angle alpha does its roof make?
• Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
• Tiles
How many square tiles with an area of 121 cm2 have to be ordered for the square room's paving with a side length of 2.75 meters?
• Tent
Pyramid-shaped tent has a base square with a side length of 2 m and a height 1.7 m. How many meters of canvas is nneded to make it if for a waste should be added 10%?
• Climb in percentage
The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km.
• Tiles
Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
• RT and ratio
A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?
• Clocks
How will long path walk the end of the clock's minute-hand long 7 cm for 330 minutes? How long will walk in the same time hour-hand?
• Cylinder - h
The cylinder volume is 140 cm3. The base radius is 7 cm. Calculate the height of the cylinder.
• Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
• Sphere slices
Calculate the volume and surface of a sphere if the radii of parallel cut r1=31 cm, r2=92 cm, and its distance v=25 cm.
• Map scale
The rectangular plot has a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
• Sector
The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.

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