📐 geometry

1. Problemet handler om at vise, at arealet af et A0-papir er cirka 1 m². 2. Arealet af et rektangel beregnes som længde gange bredde: $$A = l \times b$$

1. Problem: Vis, at arealet af et A0-papir er cirka 1 m². 2. Formlen for arealet af et rektangel er $$A = \text{længde} \times \text{bredde}$$.

1. **State the problem:** We need to find the surface area of a rectangular prism with height $h=87$ and base side length $b=54$. Since only one base side is given, we assume the b

1. **State the problem:** We are given two parallel lines cut by a transversal, forming a triangle with angles labeled $x + 25^\circ$ and $x - 5^\circ$. We need to find the value o

1. **Problem statement:** A piste is 1200 meters long down the mountain with a height difference of 450 meters. We need to find the horizontal distance (a) and the steepness of the

1. **State the problem:** We have an isosceles triangle \(\triangle LMN\) with base \(NL\). The angles are given as \(m \angle N = (2x + 33)^\circ\) and \(m \angle L = (3x + 24)^\c

1. Planteamos el problema: calcular el área de sectores circulares o sectores anulares dados los radios y el ángulo central en grados. 2. Fórmula para el área de un sector circular

1. **State the problem:** Find the area of the polygon with given side lengths and shape. 2. **Analyze the polygon:** The polygon is formed by eight connected line segments with le

1. **State the problem:** We are given a cube with a surface area of 294 cm² and need to find its volume. 2. **Recall the formulas:**

1. **State the problem:** We have a right triangle with one leg of length 11 and hypotenuse of length $x$. We need to find the length of the other leg in simplest radical form with

1. **Problem statement:** We have a right triangle with one leg labeled $x$, the other leg labeled $7$, and the hypotenuse is a side of an equilateral triangle. We need to find $x$

1. **Problem statement:** We have an isosceles right triangle with two equal sides each of length $x$ and the base side length is 1. We need to find the length of side $x$ in simpl

1. **Problem statement:** We have a square with side length $x$ and half of its diagonal labeled as $\sqrt{6}$. We need to find $x$ in simplest radical form with a rational denomin

1. **Stating the problem:** We are given two triangles with angles expressed in terms of $y$ and need to find the value of $y$. 2. **First triangle:** Angles are $y^\circ$, $3y^\ci

1. Problem statement: Find the measure of $\angle CAD$ in terms of $\angle 1$ and $\angle 2$ given that $\overline{BE}$ is parallel to $\overline{FH}$ and $\overline{AG}$ is a stra

1. **State the problem:** We are given the angle measure equation for question 37: $$m\angle 2 = 5x - 8$$ and the angle measure is $$58^\circ$$.

1. **State the problem:** We need to find the exact volumes of a cylinder and a cone, both with radius $r=7$ mm and height $h=6$ mm.

1. **State the problem:** We need to find the radius $r$ of a cone given its height $h=12$ cm and volume $V=36\pi$ cubic cm. 2. **Formula for the volume of a cone:**

1. **State the problem:** We are given a cylinder with volume $178\pi$ cubic inches. We need to find the exact volume of a cone that has the same base area and height as this cylin

1. **State the problem:** We need to find the volume of a cylinder with radius $r = 5.3$ inches and height $h = 8.4$ inches. 2. **Formula for volume of a cylinder:**

1. **State the problem:** Find the exact volume of a cylinder with radius $r=4$ inches and height $h=8$ inches. 2. **Formula:** The volume $V$ of a cylinder is given by the formula