📐 geometry

1. **Problem statement:** We have a square PQRS with points labeled clockwise: P (bottom-left), Q (top-left), R (top-right), S (bottom-right). Diagonals PR and QS intersect at U (c

1. **Stating the problem:** We need to find the total area of a composite shape consisting of a rectangle and a semicircle attached on the left side of the rectangle.

1. **Problem statement:** We have a square PQRS with points P, Q, R, S in order. Point T lies on side SR such that ST = SR, and point U is inside the square. Given angles are \(\an

1. The problem asks to find the length of segment AB given that segment AD is 13 cm. 2. To solve this, we need more information about the relationship between AB and AD, such as wh

1. The problem seems to involve points lying on the same line within a parallelogram. 2. In a parallelogram, opposite sides are parallel and equal in length.

1. The problem asks for the length of line segment AB. 2. To find the length of a line segment between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ in the coordinate plane, we use th

1. **Stating the problem:** We have a parallelogram ABCD with sides given as $AB = (3x - 5)$ cm, $BC = (2y - 7)$ cm, and $AD = (y + 3)$ cm. We need to analyze the relationships bet

1. **Problem Statement:** We have a square PQRS and point x is the midpoint of side PQ. We need to find the measure of angle $\angle ZPX$ in degrees. 2. **Understanding the problem

1. **Problem 1:** Calculate the length of the minor arc AB of a circle with radius 60 m and central angle 150°. 2. **Formula:** The length of an arc $s$ is given by $$s = r \theta$

1. **Problem statement:** We need to find the length of the arc AB of a sector OAB of a circle where the radius $r = 47$ mm and the central angle $\theta = 66^\circ$. 2. **Formula

1. **Problem statement:** We need to find the length of the minor arc AB of a circle with circumference 95 cm and central angle 72°. 2. **Formula:** The length of an arc $L$ is giv

1. **State the problem:** We are given the surface area of a sphere as $196\pi$ cm$^2$ and need to find the radius $r$ of the sphere. 2. **Formula:** The surface area $A$ of a sphe

1. **State the problem:** We need to find the total surface area of a cone with radius $r=4$ cm and slant height $l=5$ cm, expressed in terms of $\pi$. 2. **Recall the formulas:**

1. **State the problem:** Given two parallel lines $m \parallel n$ and a transversal, we have corresponding angles $120^\circ$ and $(5x + 20)^\circ$. We need to find the value of $

1. **Problem Statement:** Given three parallel lines $l \parallel m \parallel n$ and a transversal crossing them, the angles between $l$ and $m$ and between $m$ and $n$ are given a

1. حل المعادلة: 0 = 3(x - 2) في مجموعة الأعداد Q. - نبدأ بكتابة المعادلة: $$0 = 3(x - 2)$$

1. **Problem Q5:** In parallelogram □ABCD, AB is extended to E such that BE = AS. Prove DE bisects BC. 2. **Formula and rules:** In parallelograms, opposite sides are equal and par

1. **State the problem:** We need to show that the triangle with vertices A(2, 3), B(5, 7), and C(8, 3) is isosceles, meaning exactly two sides are equal in length. 2. **Formula us

1. **Problem Statement:** Find the measure of the indicated angles for problems 21 to 27 given the angle expressions. 2. **Key Concepts:**

1. সমস্যাটি হলো: ১০ কেভি লম্বা এলাকা কত বর্গমিটার হবে? 2. এলাকা নির্ণয়ের সূত্র:

1. **State the problem:** We need to approximate the measure of angle $\angle Q$ in a right triangle with given side lengths. 2. **Given:**