Pythagorean theorem + area - practice problems - page 15 of 32
Number of problems found: 622
- Rectangle
In a rectangle with sides, 8 and 9 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than any side of the rectangle? - Inscribed circle
Write the equation of an incircle of the triangle KLM if K [2,1], L [6,4], M [6,1]. - Square
Points A[9,9] and B[-4,1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Determine 82394
Determine the equation of the circle that passes through the point M(-1,2) and N( 3,0) and whose center lies on the line p: x=-3+t, y=-1+t,
- 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) - Calculate 16223
The following elements are known in the right triangle ABC: a = 10 cm, height to side c h = 9.23 cm. Calculate o, R (radius of the inscribed circle), r (radius of the inscribed circle). - 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 - Calculate 82144
Calculate the height of side b (v_b) of triangle ABC with vertices A[4;1;3] B[2;3;3] and C[1;1;3]. - Calculate 66814
Calculate the area and perimeter of the right triangle ABC if A [5.5; -2.5] B [-3; 5] C [-3; -2.5]
- A circle 2
A circle is centered at the point (-7, -1) and passes through the point (8, 7). The radius of the circle is r units. The point (-15, y) lies in this circle. What are r and y (or y1, y2)? - Calculate 6
Calculate the distance of point A[0, 2] from a line passing through points B[9, 5] and C[1, -1]. - Quadrilateral PQRS
PQRS is a quadrilateral with P(4,4), S(8,8), and R(12,8). If vector PQ=4*vector SR, find the coordinates of Q. Solve it - Vertex points
Suppose the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area. - Equation 81932
Write the general equation of a circle with point S(2;5) and point B(5;6) lying on this circle.
- Pentagonal pyramid
Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm. - Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m. The pyramid height is 1.6 m. How many square meters of sheet metal are needed to cover the top of the tower if 15% extra sheet metal is needed for join - Pit
The pit has the shape of a truncated pyramid with a rectangular base and is 0.8 m deep. The pit's length and width are the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of the pit, we use 0.6 l of green color. How many liters of paint are ne - Iglu - cone tent
The cone-shaped tent is 3 m high, and the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m² of fabric is needed for production (including flooring) if 20% needs to be added to the minimum amount due to cutting waste - Traffic cones
Forty identical traffic cones with a base diameter d = 3 dm and a height v = 6 dm should be painted on the outside with orange paint (without base). How many crowns do we pay for color? If we need 50 cm³ of paint to paint, 1m² and 1l of paint cost CZK 80?
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