📐 geometry

1. **State the problem:** We need to find how many smaller cuboid boxes (10 cm by 3 cm by 4 cm) fit completely inside the larger cuboid box (50 cm by 30 cm by 20 cm). 2. **Formula

1. **Problem statement:** We have a pentagon and a triangle sharing a side. We know the pentagon's angles: 107°, 31°, 102°, and 62°, and the triangle's angles: 79° and $k$. We need

1. **Stating the problem:** We have a shape $R$ translated by the vector $$\begin{pmatrix} 2 \\ -6 \end{pmatrix}$$ to get shape $R'$. Then $R'$ is translated to get shape $R''$. We

1. **Problem Statement:** Given a parallelogram ABCD with diagonals intersecting at O, where $\angle CD = 13\frac{6}{3}$ (interpreted as $13 + \frac{6}{3} = 15$ degrees), and $OD$

1. Énoncé du problème : On considère un triangle ABC rectangle en A avec AB = 2 et BC = x.

1. **Problem Statement:** We are given that line X contains the hypotenuses of two similar triangles LMN and PQR. The slope of line X between points (-7, 6) and (-4, 4) is given as

1. **Problem Statement:** Given quadrilateral ABCD with AB \parallel DC, \(\angle BDC = 30^\circ\), and \(\angle BAD = 80^\circ\), find the values of \(x = \angle ABC\), \(y = \ang

1. **Problem statement:** We have a right triangle XYZ with a right angle at vertex Y. The side XY is 9 cm, the hypotenuse XZ is 17 cm, and we need to find the length of side YZ. 2

1. **State the problem:** We need to find the length of the hypotenuse in a right-angled triangle where the two perpendicular sides measure 2 cm and 1.5 cm. 2. **Formula used:** Ac

1. **Problem statement:** We need to find the length of the hypotenuse in a right-angled triangle where one angle is 60° and the side opposite this angle is 6 meters. 2. **Formula

1. **Problem Statement:** Given trapezium ABCD with AB || DC, \(\angle BDC = 30^\circ\), and \(\angle BAD = 80^\circ\). We need to find the values of \(x\), \(y\), and \(z\) where

1. **Problem Statement:** Find the value of $x$ if $AOB$ is a straight line. 2. **Understanding the problem:** A straight line measures $180^\circ$. The angle $AOB$ is formed by po

1. **Problem statement:** We have a sector OAXB of a circle with center O and radius 10 cm. Chord AB has length 12 cm, M is midpoint of AB, and OX is perpendicular to AB passing th

1. **Stating the problem:** We are given three angles around point E: 80°, 20°, and an unknown angle $x$. We need to find the value of $x$. 2. **Understanding the setup:** The angl

1. **Stating the problem:** We are given three angles at point E: $x^\circ$, $80^\circ$, and $160^\circ$. The angle $x^\circ$ is between the horizontal line EA and the vertical lin

1. **Stating the problem:** We are given a point G where two perpendicular lines intersect, forming a right angle of 90°. 2. The horizontal line passes through points A and B, and

1. The problem is to find the volume of a prismatoid using the prismatoid formula. 2. The prismatoid volume formula is:

1. **Problem Statement:** We have a solid with vertices A, B, C, D, E. The face angles at A and B are right angles (90⁰). Given $AB=3$ m, vertex E lies in the plane CAD, and edges

1. **Problem Statement:** Given three chords AB, CD, and EF of equal length in a circle with center O, and points L, M, N on AB, CD, EF respectively such that OL \perp AB, OM \perp

1. **Problem 1: Find the volume of the rectangular prism with dimensions 5 cm, 10 cm, and 2 cm.** The volume $V$ of a rectangular prism is given by the formula:

1. **Problem 1: Find the size of angle FOE.** Given rays from point O with angles 87°, 45°, and 45° between some rays, and points labeled A, B, C, D, E, F around O.