📐 geometry

1. **Problem Statement:** Find the perimeter of the first shape (a) with given sides. 2. **Given:**

1. **State the problem:** We have a circle with center A, and an arc BC whose length is \(\frac{2}{5}\) of the entire circumference. We need to find the central angle \(x^\circ\) s

1. **State the problem:** We need to find the area of a sector of a circle with radius $9$ cm and central angle $140^\circ$. 2. **Formula for the area of a sector:**

1. Planteamos el problema: Tenemos los puntos $A(2,3)$ y $B(12,7)$ y un punto $P(x,y)$ tal que $PB = 2AP$. 2. Usamos la fórmula de distancia entre dos puntos: $$d = \sqrt{(x_2 - x_

1. **Problem statement:** In triangle ABC, AD and AE are the altitude and median to side BC respectively, with AD = 1 and AE given. It is also given that the angles at A are equal:

1. The problem asks to calculate the value of $n$ and the interior angles of two regular polygons with sides $n-1$ and $n$ respectively, given that the sum of their interior angles

1. **Problem statement:** Given a circle M with diameter length 12 cm, radius $r=6$ cm, and points such that $MC=CB$ and $AC = BC + 1$ cm, find the length of $AB$. 2. **Known facts

1. **Problem:** Given points A (1, 3), B (-2, -1), and C (3, -1), find the coordinates of the vertices of triangle ABC and calculate its area. 2. **Vertices:** The vertices are giv

1. **State the problem:** We need to find the distance between two points $A$ and $B$ on a Cartesian plane. 2. **Formula:** The distance between points $A(x_1, y_1)$ and $B(x_2, y_

1. **Problem statement:** Find the length $x$ in each right triangle using the Pythagorean theorem, correct to 1 decimal place. 2. **Formula:** For a right triangle with legs $a$,

1. The problem is to draw a cube, which is a three-dimensional geometric shape with six equal square faces. 2. A cube can be represented in 2D by drawing a square and then drawing

1. **State the problem:** We need to find the length of one edge of a cube given its volume is 64 cm³. 2. **Formula:** The volume $V$ of a cube with edge length $s$ is given by:

1. **Problem Statement:** We have two similar triangles ABC and DEF. Given sides are $AB=3$ cm, $BC=4$ cm, and $DE=6$ cm. We need to find the length of side $EF$. 2. **Formula and

1. **State the problem:** We have two similar triangles ABC and DEF. Given sides $AB=3$ cm, $BC=4$ cm, and $DE=6$ cm, we need to find the length of side $EF$. 2. **Recall the prope

1. **Problem 1.a:** In parallelogram ABCD, given that angle \(\angle DAB = 60^\circ\), find angle \(\angle C\). 2. **Formula and properties:** In any parallelogram, opposite angles

1. **Problem Statement:** In parallelogram ABCD, we are given that angle \(\angle DAB = 60^\circ\). We need to find the measure of angle \(\angle C\).

1. **State the problem:** We need to find the total area of the two shaded faces of a cuboid with dimensions 7 cm (height), 9 cm (width), and 12 cm (length). The shaded faces are t

1. **State the problem:** Calculate the areas of faces A, B, and C on a cuboid with given dimensions. 2. **Identify the dimensions:**

1. **Problem statement:** Given a rectangular prism with side lengths $a=11.6$ cm, $b=9.7$ cm, and $c=14.3$ cm, and $M$ as the midpoint of segment $SR$, calculate the size of angle

1. The problem asks to find the value of angle $B$ in the context of a square ABCD with side length 22 cm and an inscribed circle. 2. Since ABCD is a square, all its interior angle

1. The problem asks to identify the type of quadrilateral ABCD. 2. To determine the type of quadrilateral, we need information such as side lengths, angles, or coordinates of point