📐 geometry

1. **State the problem:** We need to find the area of a figure composed of a rectangle and two semicircles attached on the shorter sides. 2. **Identify given dimensions:** The rect

1. **State the problem:** Find the area of a composite figure made of a parallelogram and a semicircle. 2. **Identify given dimensions:**

1. **State the problem:** We need to find the area of a composite figure made of a rectangle and two semicircles attached to the shorter sides of the rectangle. 2. **Identify given

1. **Énoncé du problème :** Nous avons un carré ABCD avec deux triangles équilatéraux AEB et BCF. Il faut déterminer la nature des triangles ADE et EBF, démontrer une mesure d'angl

1. **Énoncé du problème** : Nous avons un carré ABCD orienté dans le sens direct, avec deux triangles équilatéraux AEB et BCF. Il faut déterminer la nature des triangles ADE et EBF

1. **State the problem:** We need to find the surface area (area) of a scalene triangle with base $b = 5$ cm and height $h = 9$ cm. 2. **Formula:** The area $A$ of a triangle is gi

1. The problem asks to find the surface area (SA) of a given figure. 2. From the information, the figure includes a scalene triangle with base $b=9$ cm and height $h=5$ cm.

1. **Problem statement:** Tarzan wants to find the width of the river, which corresponds to the vertical distance from point A to point B. 2. **Setup:** We have a right triangle fo

1. The problem is to find the final coordinates of a point after rotation on a graph. 2. The formula for rotating a point $(x,y)$ by an angle $\theta$ counterclockwise about the or

1. **State the problem:** We have a triangle with vertices A(0, 2), B(-10, 1), and C(-9, 6). We need to rotate this triangle 270° clockwise about the origin. 2. **Formula for rotat

1. **Problem statement:** We have a circle with center at point $O(0,0)$ and a point $N(1,0)$ on the circle. Point $M(a,b)$ is also on the circle. The angle $\angle NOM$ measures $

1. **Problem statement:** Given triangle ABC with points A(8,0), B(0,0), and angle $\angle BAC = 300^\circ$, two points start moving simultaneously: one from A towards C along AC a

1. **State the problem:** We have a large rectangle divided into 20 small squares (5 rows × 4 columns). Each small square has an area of $9\text{ cm}^2$. Among these, 11 squares ar

1. **State the problem:** We have four intersecting lines forming two pairs of parallel lines cut by two transversals, creating angles 49° and 58° at the top left, and unknown angl

1. **State the problem:** We have two intersecting lines forming angles 120°, $x$, and 125°. Angle $x$ is opposite the 120° angle, and angle $y$ is adjacent to the 125° angle. We n

1. **Problem:** Find the volume of a cylinder with radius 6 cm and height 5 cm, using $\pi = 3.14$. 2. **Formula:** The volume $V$ of a cylinder is given by

1. **Stating the problem:** We are given points of a quadrilateral with vertices \(A(1,3), B(4,1), C(6,4), D(3,6)\) and vectors \(\vec{u} = \overrightarrow{AB} = (3, -2)\) and \(\v

1. **Problem Statement:** Given that angle 1 is congruent to angle 8 ($\angle 1 = \angle 8$), determine which lines are parallel. 2. **Understanding the Setup:** Lines $l$ and $m$

1. **Problem statement:** Given that the pairs of angles \(\angle 13 = \angle 2\), determine which lines are parallel. 2. **Understanding the problem:** When two lines are cut by a

1. The problem seems to involve understanding the relationship between the hypotenuse (hp) and the side length of a right triangle. 2. In a right triangle, the hypotenuse is the lo

1. **State the problem:** We need to find the value of $x$ such that point $N$ is the incenter of triangle $QRP$. The incenter is the point where the angle bisectors intersect and