# 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: 1949

• Flowerbed We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius.
• Track arc Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?
• Cap Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 cm.
• Cuboid box How many m2 paper is needed for the sticking cuboid box of dimensions 50 cm, 40 cm and 30 cm? To the folds add one-tenth the area.
• Rectangle - sides What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?
• Ratio of edges The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
• Paint cans How many paint cans do we need to paint the floor in two rooms with dimensions of 6.8m x 4.5m and 6m x3.8m? One can arefor 6m².
• Triangular prism Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm
• Surface and volume od cuboid Content area of the square base of cuboid is Sp = 36 cm2 and its height 80 mm. Determine its surface area and volume.
• Inner angles The magnitude of the internal angle at the main vertex C of the isosceles triangle ABC is 72°. The line p, parallel to the base of this triangle, divides the triangle into a trapezoid and a smaller triangle. How big are the inner angles of the trapezoid?
• Isosceles triangle The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
• Square room What is the size of the smallest square room, which can pave with tiles with dimensions 55 cm and 45 cm? How many such tiles is needed?
• Rectangle 39 Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)
• Circle arc Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of the central angle.
• Lookout tower Calculate the height of a lookout tower forming a shadow of 36 m if at the same time a column 2.5 m high has a shadow of 1.5 m.
• Equilateral cylinder Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
• Tower How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°? Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
• Conical area A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
• Plane II A plane flew 50 km on a bearing 63degrees20 and the flew on a bearing 153degrees20 for 140km. Find the distance between the starting point and the ending point

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