📐 geometry

1. **State the problem:** We are given a rectangle MNOL with sides labeled as follows: top side MN = 26, bottom side LO = 26, left side ML = 5a - 7, right side NO = 2a + 8, and ang

1. **Problem Statement:** Find the length AB of rhombus FGHI given the side length expressions. 2. **Recall Properties of a Rhombus:** All sides are equal in length.

1. **Problem 4:** In a right triangle, one acute angle is 9 times the other. Find each acute angle. 2. The sum of acute angles in a right triangle is 90° because the right angle is

1. **Problem statement:** We have a chessboard divided into four pieces: two right triangles and two trapezoids. Each small square has area 1 unit. We need to find the area of each

1) Problem 1: Given angles with expressions in terms of $x$ and $y$, find $y$ when $x=20$. 2) Problem 2: Given segment lengths with expressions in terms of $x$ and $y$, find $x$, $

1. **State the problem:** Find the distance $d$ between points $A(-5,5)$ and $B(5,-5)$ on the coordinate plane. 2. **Formula:** The distance between two points $(x_1,y_1)$ and $(x_

1. **State the problem:** Find the distance $d$ between points $A=(11,-5)$ and $B=(1,7)$ on the coordinate plane. 2. **Formula:** The distance between two points $(x_1,y_1)$ and $(

1. **State the problem:** We have a right triangle with legs measuring 10 cm and 24 cm, and we need to find the hypotenuse $x$ using Pythagoras' theorem. 2. **Formula:** Pythagoras

1. **State the problem:** Find the distance between the points $(0,0)$ and $(-6,5)$. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given b

1. **State the problem:** Calculate the area of a trapezium with parallel sides of lengths 7 cm and 3 cm, and a height of 6 cm. 2. **Formula for the area of a trapezium:**

1. The problem asks for the mathematical name of the 3D shape and the number of its faces. 2. The shape described is a hexagonal prism, which is a type of prism with hexagonal base

1. **Problem Statement:** Find the measures of the other angles of a parallelogram if one angle measures 78°.

1. **Stating the problem:** We have a sequence of T-shaped patterns made of square tiles each with side length 1 cm. - Pattern 1 has 5 tiles: a horizontal row of 3 tiles and a vert

1. Let's start by stating the problem: We want to understand the theorems related to isosceles and equilateral triangles. 2. **Isosceles Triangle Theorem:** This theorem states tha

1. **Stating the problem:** Construct triangle $\triangle ABC$ and draw its circumcircle for the given cases.

1. সমস্যাটি হলো: একটি সুষম ষড়ভুজের কেন্দ্র থেকে শীর্ষবিন্দুগুলোর কেন্দ্রস্থ কোণের মান নির্ণয় এবং ক্ষেত্রফল বের করা। 2. সুষম ষড়ভুজের প্রতিটি কেন্দ্রস্থ কোণের মান নির্ণয়ের সূত্র হল

1. **Problem statement:** We are given triangle $\triangle EFG$ with incenter $S$, where angle bisectors $ES$, $FS$, and $GS$ meet. Points $P$, $Q$, and $R$ are the feet of perpend

1. **State the problem:** We need to find the area of quadrilateral ABCD with sides AB = 7 cm, BC = 15 cm, CD = 25 cm, diagonal AC = 20 cm, and a right angle at vertex C. 2. **Anal

1. **Stating the problem:** We have a scale drawing where 1 cm represents 100 km.

1. **Problem Statement:** Calculate the cost to fill a cylindrical water drum with radius 0.3 m and height 1 m, given water costs 50 per cubic meter. 2. **Formula:** The volume $V$

1. **Problem Statement:** Find the angle between the diagonal $AG$ and the plane $EFGH$.