Pythagorean theorem + area of a shape - practice problems - page 14 of 23
Number of problems found: 458
- Circle - analytics geometry
Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0. - Calculate 35083
Draw an isosceles triangle ABC with a base 7 cm long and shoulders 5.5 cm long. Assemble all the heights, measure them, and calculate their sum. - Right triangle from axes
A line segment has its ends on the coordinate axes and forms a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment? - Triangle KLB
It is given equilateral triangle ABC. From point L, the midpoint of the side BC of the triangle, it is drawn perpendicular to the side AB. The intersection of the perpendicular and the side AB is point K. How many percents of the area of the triangle ABC
- 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 - 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 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]
- 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. - 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
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