📐 geometry

1. **Problem Statement:** Moira walked 3.5 km west and then 4.5 km north from her house. We need to find the straight-line distance from her current position back to her house. 2.

1. **Stating the problem:** We have a right triangle \(\triangle ABC\) inscribed in a circle where \(CA\) is the diameter. We need to identify the hypotenuse, adjacent, and opposit

1. **Problem Statement:** Calculate the area of a hexagonal sun deck with a top side length of 40 cm, a bottom side length of 96 cm, and a vertical height of 90 cm. 2. **Formula Us

1. **הבעיה:** נתון מעוין ABCD ונקודה M על האלכסון AC כך ש- MD = MC. 2. **הוכחת M מרכז המעגל החוסם את המשולש DBC:**

1. Problem: Find the number of things which coincide with one another. 2. The question asks: "The things which coincide with one another are?" with options a)0 b)1 c)2 d)3.

1. **State the problem:** We have a larger square with side length 18 cm and a smaller square carpet inside it with side length 9 cm. The carpet is centered, and there is a 1 cm ma

1. **State the problem:** We need to find the depth of the water in a rectangular cuboid container given the volume of water in milliliters (ml). Since 1 ml = 1 cm³, the volume of

1. **State the problem:** We need to find the volume of a cuboid with given dimensions. 2. **Given:**

1. **Problem:** Two similar triangles have the ratio of their corresponding sides as 3:4. Find the ratio of their areas. 2. **Formula and Rules:**

1. **Problem statement:** Given the diagram with points F, E, D, A, B, C and angles \(\angle CED = 24^\circ\) and \(\angle BAE = 60^\circ\). Lines EA and EC bisect \(\angle FEB\) a

1. Let's start by stating the problem: We want to solve a geometry problem, but since the exact problem isn't specified, let's consider a common geometry problem such as finding th

1. **Stating the problem:** You asked why we assume that the lines EA and EC bisect the angles, and whether only perpendicular bisectors divide angles into two equal parts.

1. **Stating the problem:** We are given a geometric figure with points F, E, D, A, B, and C.

1. بين أن المستقيمين (HK) و (LN) متوازيان. - إذا كان OH عمودياً على HK و OH = 3.6 cm، و HK = 3 cm، و KN = 5.4 cm، و KH = 2 cm، فإن الزوايا المتقابلة متساوية مما يدل على توازي (HK)

1. نبدأ ببيان المسألة: لدينا مثلث قائم الزاوية في K، حيث طول الوتر IJ = 13 سم، والزاوية x عند النقطة J تساوي 25°. 2. نستخدم قانون جيب التمام أو قوانين المثلثات القائمة لحساب طول ال

1. **State the problem:** We need to find the area of a segment of a circle with radius $12$ cm and a central angle of $60^\degree$. 2. **Formula and explanation:** The area of a s

1. **Problem:** Construct a rectangle in which one of the diagonals divides the angles into 30° and 60°. 2. **Understanding the problem:** In a rectangle, all angles are 90°. The d

1. **State the problem:** Find the perimeter of a square with side length 3.5 cm. 2. **Formula:** The perimeter $P$ of a square is given by

1. **State the problem:** Find the area of a triangle with base 12 cm and height 9 cm. 2. **Formula:** The area $A$ of a triangle is given by the formula:

1. The problem is to find the area of a parallelogram given its base and height. 2. The formula for the area of a parallelogram is $$\text{Area} = \text{base} \times \text{height}$

1. **Stating the problem:** We are given the cosine rules for angles in a triangle: $$\cos A=\frac{b^2+c^2-a^2}{2bc}$$