Planimetry - math word problems - page 100 of 187
Number of problems found: 3735
- Triangle height intersection
Given a triangle ABC: A (-1,3), B(2,-2), C(-4,-3). Determine the coordinates of the intersection of the heights and the coordinates of the intersection of the axes of the sides. - Trapezoid plot area
The right trapezoidal plot has a basic length of 102 m and 86 m. The vertical arm is 63 m long. Calculate the plot’s area and the mesh consumption for its fencing. - Isosceles trapezoid
In an isosceles trapezoid, the basic lengths are 15 cm and 9 cm. The diagonals are 13 cm long. Calculate the perimeter and area of the trapezoid. - Seed drills
The tractor driver connected two seed drills behind the tractor and sowed 7 ha of grain in 5 hours. How many hectares did he plant in 8 hours the next day if he connected three seed drills? - Angles - clock hands
Find the angle that the large hand makes with the small hand of the clock - the central angle at 12:30. Find the magnitude of the smaller angle (if possible). (Help: it's enough if you calculate how big an angle the hands make if they are 1 minute apart. - Mirror
How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm, and Paul is from the tower distance of 20 m. - Hairs
Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix for the 3.6 amino acid residues - Luiza
Luiza delivers newspapers in her neighborhood. If you plot the points (-1, 1), (4, 1), (4, -2), and (-1, -2), you will create a representation of the route she takes in miles. How many miles does her route cover? - Two tangents
The figure shows a circle k with centre S and radius 5 cm, and a point A which is 13 cm from centre S. From point A, two tangents p and q are drawn to circle k, with points of tangency P and Q. In addition, another tangent t is drawn to circle k, intersec - Triangle perimeter similarity
Calculate the perimeter of triangle ABC if you know that it is similar to triangle EFG in which e=144 mm, f=164 mm, g=92 mm, and the similarity ratio is 4. Express the result in cm. - Circular segment
Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm, and the angle α = 60°. Help formula: S = 1/2 r². (Β-sinβ) - Building shadow height
The school building casts a shadow 16 m long on the plane of the yard, and at the same time, a vertical meter pole casts a shadow 132 cm long. Determine the height of the building. - The amphitheater
The amphitheater has the shape of a semicircle, the spectators sit on the perimeter of the semicircle, and the stage forms the diameter of the semicircle. Which spectators, P, Q, R, S, and T, see the stage at the greatest viewing angle? - Polygon angle
A regular 15-angle is given. A triangle is formed if we connect points 3 and 7, 13 and 10. The vertices are 3 and 13, and the lines' intersections are 3.7 and 13.10. We are to determine the angle size formed by sides 3.7 and 13.10. These numbers indicate - Touch circle
Point A has a distance (A, k) = 10 cm from a circle k with radius r = 4 cm and center S. Calculate: a) the distance of point A from the point of contact T if the tangent to the circle is drawn from point A b) the distance of the contact point T from the l - Minute hand distance
The distance between the tip of the minute hand and the center of the dial is 12 mm. Determine the distance traveled by the tip in 45 min. (draw a clock face and a minute hand and realize the distance it will cover in 45 min.) - Viewing Two Poles
Two straight paths cross, making an angle alpha = 53 degrees 30'. There are two pillars on one of them, one at the intersection, the other at a distance of 500 m from it. How far does one have to go from the intersection along the other road to see both p - Similar triangles
In the triangle DEF is DE = 21 cm, EF = 14.7 cm, DF = 28 cm. The triangle D'E'F' is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D'E'F' if the similarity coefficient is one-seventh. - Interior angles
In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees, and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles. - The coordinates
The coordinates (5, 2) and (-6, 2) are vertices of a hexagon. Explain how to find the length of the segment formed by these endpoints. How long is the segment?
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