# 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

• Area and perimeter of rectangle
The content area of the rectangle is 3000 cm2, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
• Larger perimeter
There are a square and a circle that passes through two adjacent vertices of the square (end points of side a) and the center of the opposite side (c). Which of the plane shape has a larger perimeter?
• Body diagonal
Find the length of the body diagonal of a cuboid with edges lengths of 16 cm, 7 cm, and 4 cm.
What is the volume of a regular quadrilateral pyramid if its surface is 576 cm2 and the base edge is 16 cm?
What is the volume of a regular quadrilateral pyramid if the edge of the base is 8 cm long and the height of the side wall is 5 cm?
• Isosceles trapezoid
Find the area of an isosceles trapezoid, if the bases are 12 cm and 20 cm, the length of the arm is 16 cm
• Isosceles triangle
In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
• Round table
A tablecloth should be sewn on a round table with a diameter of 78 cm, which should extend around the table by 10 cm. How many cms of ribbons need to be bought for edging?
• Find the
Find the content of a regular 12 sided polygon if its side a = 12 cm.
• Vertical rod
The vertical one-meter-long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long at the same time.
• Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
• Three points
Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d
• Brass sphere
Find the weight of a brass ball with an outer radius of 12 cm, a wall thickness of 20 mm if the brass's density is 8.5 g/cm3.
• The straight
The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m?
• 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.
• Cylindrical tank
9.6 hl of water is poured into a cylindrical tank with a bottom diameter of 1.2 m. What height in centimeters does the water reach?
• Extending square garden
Mrs. Petrová's garden had the shape of a square with a side length of 15 m. After its enlargement by 64 m2 (square), it had the shape of a square again. How many meters has the length of each side of the garden been extended?
• Gears
The front gear on the bike has 32 teeth and the rear, on the wheel, has 12 teeth. How many times does the bike's rear-wheel turn if you turn the right pedal 30 times? What distance will you go if the circumference of the bicycle wheel is 250 cm?
• Natural fertilizer
The rectangular garden measuring 120m and 60m was fertilized with 16kg of natural fertilizer. Natural fertilizer contains 45% organic matter. How much organic matter falls on 1 m2 of garden?
• Truncated pyramid
The concrete pedestal in the shape of a regular quadrilateral truncated pyramid has a height of 12 cm, the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base.

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