📐 geometry

1. **Problem (a):** Rectangular prism with length $10$ cm, width $6$ cm, height $8$ cm. - Cross-sectional area (base area) $= \text{length} \times \text{width} = 10 \times 6 = 60$

1. **Phát biểu bài toán:** Cho tam giác đều ABC và các điểm M, N, P trên các cạnh BC, CA, AB sao cho - BM = k \cdot BC

1. Problem: Given square ABCD is congruent to square PQRS and side AB = 4 cm, find the length of side QR. Since congruent squares have equal corresponding sides, QR = AB = 4 cm.

1. **Stating the problem:** A semi-circle has a perimeter of 100 m. We want to find the length of the diameter in centimeters. 2. **Understanding the perimeter of a semi-circle:**

1. The problem states that a semi-circle has a perimeter of 100 m and asks to find the length of the diameter in cm. 2. The perimeter $P$ of a semi-circle consists of the diameter

1. **State the problem:** We have an open rectangular box with length $1$ m, width $70$ cm, and depth $50$ cm. 2. **Convert all dimensions to meters:**

1. مسئله داده شده این است که نقطه A با مختصات (7,6) راس یک متوازی الاضلاع است که دو ضلع آن روی خطوط $$3x - 2y = 11$$ و $$4x + 3y = 8$$ قرار دارند. باید مختصات وسط قطر این متوازی ال

1. **Stating the problem:** We are given two angles that are supplementary. This means their sum is $$180^\circ$$. 2. Let the smaller angle be $$x$$. Then the larger angle is three

1. Let's state the problem: A regular hexagon has several lines of symmetry, and we want to find how many lines of symmetry it has and the angle between any two adjacent lines of s

1. **Problem statement:** We have a circle with center $O$ and a tangent line $\overleftrightarrow{AC}$ at point $C$ on the circle. 2. Given that $\angle BAC = 23^\circ$, and since

1. The problem asks for the area of a quarter circle with radius $4$ units. 2. The area of a full circle is given by the formula $$A=\pi r^2$$ where $r$ is the radius.

1. The problem asks for the area of a semicircle with radius 6 units. 2. The formula for the area of a full circle is $$A = \pi r^2$$ where $r$ is the radius.

1. **State the problem:** Given that angle A is circumscribed about circle O, find the measure of \(\angle A\) given that the central angle \(\angle BOC = 92^\circ\). 2. **Recall t

1. The problem gives a triangle ABC with sides AB = 24 units, AC = 10 units, and BC = 5 units. 2. The circle P inside the triangle is tangent to all three sides, meaning it is the

1. The problem states that $\angle AOC$ is a central angle and intercepts arc $\widehat{AC}$. The measure of a central angle is equal to the measure of the intercepted arc.\n\n2. G

1. **State the problem:** We are asked to determine whether the measure of an intercepted arc of an inscribed angle is one half the measure of the inscribed angle. 2. **Recall the

1. Statement of problem: Find the radius, diameter, center, and other circle parts as labeled, then solve algebraic problems involving central and inscribed angles. 2. Definitions:

1. Stating the problem: We need to find the total surface area enclosing the region common to the three cylinders given by $$x^2 + y^2 = 3^2, \quad x^2 + z^2 = 3^2, \quad z^2 + y^2

1. Problem: Find the image of point A(−1, 3) after reflection about the line $x=4$ followed by reflection about the Y-axis. Step 1: Reflect A about $x=4$. The formula for reflectio

1. We are given a triangle ABC with vertex C at the top and an isosceles triangle where sides AC and BC are equal. 2. The measure of angle m(AB) is given as $\frac{1}{4}$ of the le

**Exercice 1 :** Soit ABC un triangle, et D un point tel que $\vec{AD} = \vec{AB} - \vec{AC}$.