📐 geometry

1. **Problem:** Find the radius of a cylinder with height $27$ mm and volume $4300$ mm$^3$. 2. **Formula:** The volume $V$ of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is

1. **Nyatakan masalah:** Diberi sektor bulatan OABC dengan OA = AC = 6 cm dan DC adalah lengkok sukuan bulatan. OD adalah pembahagi dua sama serenjang perentas AC.

1. **Stating the problem:** We have points A, B, C, and D on a school land plot with given distances and angles. We need to find the required gravitational force (or weight) and re

1. The problem asks to find the value of angle R in a regular polygon with five sides (a regular pentagon). 2. In a regular polygon, all interior angles are equal. The formula to f

1. مسئله: دو مثلث با اضلاع 5, 12, 13 و 5.58, 18, 13.2 داده شده‌اند که متشابه هستند. باید مساحت مثلث بزرگ‌تر را پیدا کنیم. 2. ابتدا بررسی می‌کنیم که آیا این دو مثلث متشابه هستند یا

1. **State the problem:** We need to find the area of a composite shape made of two polygons: a quadrilateral on the left and a triangle on the right. 2. **Identify the shapes and

1. **Problem statement:** Determine the unknown side lengths and angles in the similar triangles given. 2. **Given:** Triangles with sides and angles: one triangle with side 22 m o

1. **Problem statement:** We have trapezoid ABCD with an angle bisector \(\overline{AC}\) dividing it into two similar triangles \(\triangle ABC\) and \(\triangle ACD\). Given legs

1. **Problem Statement:** Design orthogonal, isometric, and perspective drawings of a greenhouse with given dimensions and scales. 2. **Given Data:**

1) a) **Show that $\angle FEM = \angle MAB$.** 1. We are given that $G$ is the symmetric of $E$ with respect to $F$, and $C$ is the symmetric of $A$ with respect to $B$.

1. **Problem statement:** Given an isosceles triangle $\triangle ABC$ with $AB = AC$. Points $D$ and $E$ are taken on the rays opposite to $BC$ and $CB$ respectively such that $BD

1. **Problem statement:** In triangle PQR, angles R and Q are bisected by lines RU and QS respectively. Given that angle P = 50° and angle TRS = 32°, find the measure of angle QTU.

1. **Problem statement:** Given rectangle ABCD with diagonal BD, trace lines D₁ and D₂ perpendicular to BD at points A and C respectively.

1. The problem is to draw a combined figure of a cylinder and a cone. 2. A cylinder is a 3D shape with two parallel circular bases connected by a curved surface.

1. **Problem statement:** Given two sides of a triangle with lengths 5.7 cm and 7.5 cm, and the angle opposite the side of length 7.5 cm is 105 degrees, find the unknowns of the tr

1. The problem is to find the area of plane shapes. 2. The formula for the area depends on the shape. For example, for a rectangle, the area $A$ is given by:

1. **State the problem:** We are given a right triangle $PQR$ with right angle at $R$. A perpendicular segment $TR$ is drawn from $R$ to $PQ$, forming two right angles at $T$ and $

1. The problem asks for the volume of a right rectangular pyramid with base length 12 feet, base width 9 feet, and height 18 feet. 2. The formula for the volume $V$ of a right rect

1. **Problem statement:** Given a circle with center O and two chords forming two angles on the circumference, one angle is 100° and the other is $x^\circ$. We need to find the val

1. **Problem Statement:** Given two parallelograms ABCD and ABEF standing on the same base AB and between the same parallel lines AB and FC, prove that the area of ABCD equals the

1. **Énoncé du problème :** Soit un triangle ABC non isocèle avec des points P sur la demi-droite [BA) et Q sur la demi-droite [CA) tels que $BP = CQ$ et $P \neq B$.