📐 geometry

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.

1. **Stating the problem:** We have a square with side length 8 units and four quarter circles of radius 8 units centered at each corner of the square. We want to understand the sh

1. **Problem statement:** We need to find the volume of a triangular prism where the base triangle has sides and angles given, including angle $\angle BDE = 25^\circ$, base length

1. **State the problem:** We need to find the volume of a triangular prism where the base is triangle ABD with right angle at B, and the prism height is along edge DE. Given: $\ang

1. **Problem statement:** We need to calculate the volume of the triangular prism where angle $BDE = 22^\circ$, $BD = 59$ m, and $AD = 27$ m. The prism has right angles at $B$ and

1. **State the problem:** We have a trapezium with top base $x+4$ cm, bottom base $x+2$ cm, height $x-1$ cm, and area 32 cm$^2$. We need to find the value of $x$. 2. **Formula for

1. **Problem Statement:** Given circle ⊙X with points A, B, C, D, E, F on the circumference and angles $m\angle AF = 32^\circ$, $m\angle DAC = 26^\circ$, and $m\angle BXD = 126^\ci

1. **Stel die probleem:** Ons het 'n parallelogram ABCD met punte A(-2, -6), B(4, 0), C(-1, 10) en D(x, y). Ons moet verskeie eienskappe bereken. 2. **Bereken die lengte van BC:**

1. **State the problem:** We have a circle centered at point A.