📐 geometry

1. Problem: Düzgün dördbucaqlı piramidanın yan tili 5 sm, tam səthi 16 sm²-dir. Oturacağının tərəfini tapın. 2. Formullar və qaydalar:

1. **Problem statement:** We need to find the angle between the line segment $AD$ and the horizontal base plane $ABEF$ of the triangular prism. 2. **Understanding the problem:** Th

1. The problem is to understand how to formulate questions involving a circle. 2. A circle is defined by the equation $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $ (h, k) $ is the cent

1. Let's create a problem similar to the ones described involving angles in a circle with intersecting chords. 2. **Problem:** In circle $O$, chords $AB$ and $CD$ intersect at poin

1. **Problem Statement:** Calculate the value of $x$ in a right triangle where one side adjacent to the angle $38^\circ$ is 5.7 m, and $x$ is the side opposite the $38^\circ$ angle

1. **Problem:** Calculate the perimeter of parallelogram ABCD given BC = 20 cm, BL = 10 cm, and DM = 18 cm. 2. **Recall:** In a parallelogram, opposite sides are equal in length. S

1. **Problem statement:** In the parallelogram ABCD, given BC = 20 cm, BL = 10 cm, and DM = 18 cm, calculate the perimeter of ABCD. 2. **Recall properties of parallelograms:** Oppo

1. **State the problem:** Calculate the volume of a right-angled triangular prism with legs 23 m and 38 m, and length (depth) 11 m. 2. **Formula:** The volume $V$ of a prism is giv

1. The problem is to find the area of a trapezoid with bases $b_1 = 3$, $b_2 = 2$, and height $h = 2$. 2. The formula for the area of a trapezoid is:

1. **State the problem:** We need to find the area of a parallelogram with a base of 3 meters and a vertical height of 2 meters. 2. **Formula:** The area $A$ of a parallelogram is

1. **Problem statement:** We are given a triangle with points A, B, C, and a point D on segment BC. We know $\angle DAC = \angle BAD$ and lengths $AC = 5.1$, $AB = 5.7$, and $BD =

1. **Problem Statement:** We are given a triangle with points A, B, C, and D. Segments AC = 5.5, AB = 5.3, BD = 4.1, and angles \(\angle DAC = \angle BAD = \theta\). We need to fin

1. **Problem Statement:** We are given a triangle with points A, B, C, and D inside it. We know that $\angle DAC = \angle BAD$ and the lengths $AC = 4.6$, $CD = 2.5$, and $AB = 6.8

1. **Problem Statement:** We are given a triangle ABC with point D on segment BC such that AD bisects angle A, meaning \(\angle DAC = \angle BAD\). We know the lengths \(AC = 5.9\)

1. **Problem Statement:** Given a circle with points M, N, P, O on the circumference and the following angles: $m \angle MN = 122^\circ$, $m \angle NO = 58^\circ$, and $m \angle PM

1. **Problem Statement:** Is it always possible to find a square such that three arbitrary points lie on its boundary?

1. **Stating the problem:** We have a right triangle with vertices $x$, $y$, and $z$. The segment $xy$ is vertical with length 12, $yz$ is horizontal, and $xz$ is the hypotenuse. W

1. The Pythagorean theorem is a fundamental relation in geometry among the three sides of a right triangle. 2. It states that in a right triangle, the square of the hypotenuse ($c$

1. You asked for points on the graph that are exactly five units away from the origin. 2. The distance from the origin to a point $(x,y)$ is given by the formula $$\sqrt{x^2 + y^2}

1. **State the problem:** Find the distance between the points $(1,2)$ and $(4,6)$ using the Pythagorean theorem. 2. **Formula:** The distance $d$ between two points $(x_1,y_1)$ an

1. The problem asks us to find the distance between the points $(1,2)$ and $(4,6)$ using the Pythagorean theorem. 2. The distance formula between two points $(x_1,y_1)$ and $(x_2,y