# 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

- Square gardens

The gardening colony with dimensions of 180 m and 300 m is to be completely divided into equally large square areas with the largest possible area. Calculate how many such square areas can be obtained and determine the side length of the square. - Vectors abs sum diff

The vectors a = (4,2), b = (- 2,1) are given. Calculate: a) |a+b|, b) |a|+|b|, c) |a-b|, d) |a|-|b|. - How many

How many different rectangles with integer page lengths have an area S = 60 cm²? - Find the

Find the pressure exerted by a crawler tractor of mass 30 t standing on a horizontal road if the content of the contact surface of the belts with the ground is 6 m square. - Trapezoid 25

Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s. Find the length of the median of Trapezoid PART in terms of s. - Tractor wheels

The front wheel of the tractor has a circumference of 18 dm and the rear 60 dm. We will make a red mark on the lowest point of both wheels. The tractor then starts. At what distance from the start will both marks appear identically at the bottom again? - Gardens

The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, 50 m. How many meters of the fence do we need to fence a square garden? - Acute triangle

In the acute triangle KLM, V is the intersection of its heights and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM and the angle MKL is 70°. What size are the KLM and KML angles? - As shown

As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6, then the perimeter of △ BDE - Perpendicular projection

Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0. - Vertex points

Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area. - Construction

Construction the triangle ABC, if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60° and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction) - The staircase

The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase. - Ladder

How long is a ladder that touches on a wall 4 meters high, and its lower part is 3 meters away from the wall? - Quadrilateral pyramid

Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture. - Triangular pyramid

Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm. - Insulate house

The property owner wants to insulate his house. The house has these dimensions 12, and 12 m is 15 m high. The windows have 6 with dimensions 170 and 150 cm. Entrance doors are 250 and 170 cm in size. How many square meters of polystyrene does he need? - Space diagonal angles

Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Railway embankment

The railway embankment section is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m, and the height of the embankment is 4.8 m. Calculates the size of the embankment section area. - The pyramid

The pyramid with a square base is 50 m high and the height of the sidewall is 80 m. Find the endge of the base of the pyramid.

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