# 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

• Garden fence
The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced?
• Cutting circles
From the square 1 m side we have to cut the circles with a radius of 10 cm. How many discs we cut and how many percent will be waste?
• Rotatable tower
Rotatable tower situated in the city center has ground shape of a regular polygon. If the tower is rotated by 14.4° around its centerpiece it looks from the side same. Your task is to calculate at least how many vertices can have a ground plan view of the
• Logs
The trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
• Wire
One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls?
• A square base
A solid right pyramid has a square base. The length of the base edge is 4 centimeters and the height of the pyramid is 3 centimeters. What is the volume of the pyramid?
• Folded square
ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD
• Rectangle
The width of the rectangle is 65% of its length. Perimeter of the rectangle is 132 cm. Determine the dimensions of the rectangle.
• Ruler and compass
Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
• Arm-leg
Calculate the length of the base of an isosceles triangle with a circumference 224 cm if the arm length is 68 cm.
• The perimeter 2
The perimeter of the quadrilateral a = 1m b = 14/5m c = 2 3/10m d = 1 4/5m?
• 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.
• Tangents to ellipse
Find the magnitude of the angle at which the ellipse x2 + 5 y2 = 5 is visible from the point P[5, 1] .
• Cone
The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
• Triangle eq
Calculate accurate to hundredths cm height of an equilateral triangle with a side length 12 cm. Calculate also its perimeter and content area.
• Garden
Rectangular garden has a length 99 m and width 84 m. Calculate how many m2 will decrease its area if land by ornamental fence with width 30 cm.
• Circles 2
Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
• Triangle angles
In a triangle ABC the interior angle at the vertex C is twice as the internal angle at the point A. Outer angle at the point B measured 117 degrees. How big is the outer angle at the vertex A?
• Perimeter of base
The circumference of the base of the rotating cylinder is same as its height. What is the diameter and height of this cylinder with volume 1 liter?
• Tangents construct
The circle k is given k (S; 2.5 cm) and an outer line p. Construct a tangent t of the circle that has with a line p angle 60°. How many solutions have the task?

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...