📐 geometry

1. **State the problem:** We need to find the volume of a right-angled triangular prism with a triangular base having sides 21 m and 37 m at a right angle, and the prism length (de

1. প্রশ্ন: P(0,2) বিন্দুর গোলকের সমাধ্ববক নির্ণয় কর। 2. গোলকের সমাধ্ববক (radius) নির্ণয়ের সূত্র হলো:

1. **Stating the problem:** We have two lines meeting at point O with angles 68°, 124°, and 120° given. We need to determine which statement about the lines is true: whether they a

1. نبدأ ببيان المسألة: لدينا مثلث ABC مع نقاط M على AB وN على AC، وقطعتا مستقيم BC وMN متوازيتان. 2. المعطيات: AF=2، AC=8، AM=12، AB=16، AE=4، و(BC) // (MN).

1. **Stating the problem:** We are given two lines, MN and PO, and we need to determine the relationship between them: whether they are perpendicular, parallel, not parallel, or no

1. The problem asks to find the difference between angles $e$ and $f$ in the figure where two lines intersect forming four angles. 2. Given that one angle adjacent to $f$ is $124^\

1. Bài 1: Xem hình bên rồi chọn kí hiệu \(\in\) (thuộc), \(\notin\) (không thuộc) hoặc các từ "đi qua", "không đi qua" để điền vào chỗ trống sao cho hợp nghĩa. - a) \(C \in a\); \(

1. **بيان المسألة:** في التمرين الأول، نكمل الشكل الهندسي المعطى ونجيب عن الأسئلة المتعلقة بالنقاط والمسقط العمودي والعلاقات بين المستقيمات.

1. The problem asks for the area of a semicircle with a diameter of 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:** We are given the volume of a sphere as $2400$ m³ and asked to find the diameter $d$. 2. **Recall the formula for the volume of a sphere:**

1. **Problem 1:** Find the radius $r$ of a cone with height $h=12$ km and volume $V=100\pi$ km³. The volume formula for a cone is:

1. The problem asks: Which of the following is a solid figure? 2. A solid figure is a three-dimensional shape that has length, width, and height.

1. The problem asks: Which of the following is a solid figure? 2. The options are:

1. **Problem statement:** Given a right triangle with points A, B, C, and D such that triangle ABC is right-angled at A, with sides AB = 3, BC = 5, BD = \sqrt{11}, and DC = 6. 2. *

1. Énonçons le problème : Trouver le point R qui divise le segment CD selon le rapport 3:1. 2. Données :

1. **State the problem:** Determine if the triangles are congruent and by which method (SSS, SAS, AAS, ASA) or if none applies. 2. **Given:**

1. **Stating the problem:** Determine the area of the polygon in part (a) with sides 5.3 cm, 3 cm, 3.5 cm, 6.1 cm, and 2.5 cm.

1. The problem asks to write a true biconditional statement about angle bisectors. 2. A biconditional statement uses "if and only if" to show equivalence between two conditions.

1. **State the problem:** We have a right triangle with angles 45°, 30°, and 90°, and sides labeled with $p$ opposite the 45° angle and $10\sqrt{3}$ adjacent to the 30° angle. We n

1. **State the problem:** We have a right triangle with a hypotenuse of length 6 and two angles of 60° and 45°. We need to find the length of side $x$, which is opposite the 45° an

1. The problem is to find the length of the hypotenuse $c$ of a right triangle with legs measuring 6 cm and 8 cm. 2. We use the Pythagorean theorem, which states that in a right tr