📐 geometry

1. Let's start by understanding what practical geometry means. Practical geometry deals with drawing and measuring figures accurately using tools like a ruler, compass, and protrac

1. **State the problem:** We have a pyramid VABCD with square base ABCD of side 20 cm. The angle between any sloping edge (e.g., VA) and the base plane ABCD is 55°. 2. **Calculate

1. The problem is to find the surface area of a dome. 2. Typically, a dome can be modeled as a spherical cap, which is a portion of a sphere cut by a plane.

1. Stated problem: We are given a triangle with angles 75°, 43°, and an unknown angle $x$, plus an additional angle 39° related by parallel lines. 2. Since the lines are parallel,

1. The problem asks for the surface area of a dome, which is half of a sphere, with radius $r = 57$ metres. 2. The formula for the surface area of a full sphere is $4\pi r^2$.

1. **Stating the problem:** We need to find the size of angle $x$ in a triangle with given angles $87^\circ$, $45^\circ$ (exterior), and $36^\circ$.\n\n2. **Analyze the given infor

1. We are given two similar shapes, R and S. 2. Shape R has a perimeter of $180$ mm and area of $1692$ mm$^2$.

1. **Stating the problem:** We have two polygons with numbers of sides $n$ and $m$. The sum of their sides is given as $$n + m = 9$$.

1. **State the problem:** We have two similar rugs, A and B. The cleaning cost is 0.40 per square meter. Rug B costs 7.20 to clean. We need to find the area of Rug A.

1. The problem asks to explain section \(\text{ד}\) which involves calculating the area of a right triangle formed by points and line segments. 2. We are given that \(S = \frac{\te

1. **State the problem:** We have two similar shapes, F and G. Shape F has a perimeter of 14 cm and a height of 2 cm. Shape G has a height of 20 cm. We need to calculate the perime

1. **Problem Statement:** Given triangle ABC with external angles at A (angle D = 80°) and B (angle E = 40°), and CPQ = 80°, ABC = 40°, with PQ and AD parallel, find the measures o

1. We are given the task to demonstrate the Pythagorean theorem: for a right triangle with legs $a$ and $b$, and hypotenuse $c$, prove that $$a^2 + b^2 = c^2.$$ 2. Consider a right

1. **State the problem:** We need to find the area of sector OAB of a circle with radius 35 mm and sector angle 64°. 2. **Recall the formula for sector area:** The area of a sector

1. It seems you are asking about the methods used in solving a problem or in mathematics in general. 2. Geometric reasoning involves understanding properties and relationships of s

1. Let's state the problem: We have a quadrilateral with 4 equal sides and one angle of 90 degrees. We need to determine if this quadrilateral must be a square. 2. A quadrilateral

1. প্রশ্নটি বোঝা: জমির প্রস্থ কত? এখানে জমির প্রস্থ নির্ণয় করতে হবে। 2. সাধারণত, জমির আয়তনের ক্ষেত্রে প্রস্থ এবং দৈর্ঘ্যের তথ্য প্রয়োজন। প্রশ্নে শুধুমাত্র প্রস্থ জানতে চাওয়া হয

1. **State the problem:** Given a quadrilateral ABCD with four equal sides (AB = BC = CD = DA) and one right angle (\(\angle DAB = 90^\circ\)), determine if ABCD is a square.

1. সমস্যাটি হলো একটি আয়তাকার জমির দৈর্ঘ্য প্রস্থের দ্বিগুণ এবং জমির পরিসীমা ১২০ মিটার। এখানে জমির ভিতরে চারদিকে সমান পাড়বিশিষ্ট ২ মিটার বিস্তৃত একটি পুকুর রয়েছে। পুকুরের গভীরতা ৫ ম

1. **Given problem:** We have a circle with points on its circumference and angles 43° and 76°, and we need to find the reflex angle $z$. 2. **Understanding the problem:** The refl

1. Bài toán yêu cầu tính chu vi hàng rào của một mảnh vườn hình chữ nhật với chiều dài $x$ và chiều rộng $y$, biết hàng rào có chu vi $120$ mét và diện tích $S=xy$ lớn nhất. 2. Ta