📐 geometry

1. 問題陳述： 我們有邊長為5公分的正三角形，將20個這樣的三角形以邊相連的方式連接成一排，求整個圖形的周長。

1. **Problem:** Calculate the perimeter when 5 chocolate bricks, each 10 cm long and 4 cm wide, are connected horizontally. 2. **Formula:** The perimeter $P$ of a rectangle is $P=2

1. نبدأ بكتابة معادلة الدائرة العامة التي تمر بالنقاط المعطاة. معادلة الدائرة في المستوى هي: $$ (x - h)^2 + (y - k)^2 = r^2 $$

1. **State the problem:** We need to find the area of the square given the information about the two triangles inside it and one side length. 2. **Analyze the given information:**

1. **Stating the problem:** We have a right triangle PQR with \(\angle Q = 90^\circ\) and \(\angle R = 2\angle P\). We want to analyze the triangle using the given angle relationsh

1. সমস্যাটি হলো: একটি ত্রিভুজ ABC যেখানে BC = 12 সেঃমিঃ। ত্রিভুজের ভিতরে M এবং N বিন্দু AC এবং BC রেখায় অবস্থিত। ত্রিভুজ CMN এর ক্ষেত্রফল 9 বর্গ সেঃমিঃ। আমাদের AM এর মান নির্ণয় ক

1. সমস্যাটি হলো: ত্রিভুজ CMN এর ক্ষেত্রফল 9 বর্গ সেমি এবং BC = 12 সেমি, AM এর মান নির্ণয় করতে হবে। 2. প্রথমে, আমরা বুঝি যে BC = 12 সেমি এবং ত্রিভুজ ABC তে B কোণটি সমকোণ।

1. Problem: Given a triangle with BC = 12 cm and the area of triangle CMN is 9 square cm, find the length of AM. 2. Formula: The area of a triangle is given by $$\text{Area} = \fra

1. **State the problem:** Find the coordinates of the image (reflection) of the point $(-4,5)$ about the line $x + 3y - 1 = 0$. 2. **Formula and explanation:** The reflection of a

1. **State the problem:** We have a rectangular paper folded along its diagonal AB. The ratio of the area of Figure 2 (shaded part) to Figure 1 (remaining part) is 4:7. The shaded

1. **Problem statement:** Calculate the surface area of a triangular prism. 2. **Formula:** The surface area $SA$ of a triangular prism is given by:

1. The question asks if point A can have the same arc as point E. 2. In geometry, an arc is a portion of the circumference of a circle defined by two points.

1. **Problem Statement:** Given a circle with center O and points A, B, C, D, E on or inside the circle, with lines AB, BC, CD, DE, AE drawn as described, and angles $x$ at vertex

1. **State the problem:** We have a structure that is 14 ft by 14 ft in area and 16 ft in height. We want to find out how many solar panels can fit on the structure. 2. **Assumptio

1. **State the problem:** We have triangle ABC with angles $A=35^\circ$ and $B=20^\circ$. We want to find which triangles among DEF, GHI, JKL, MNO, and PQR are similar to ABC. 2. *

1. **Problem statement:** In right triangle ABC, altitude CD is drawn to the hypotenuse AB. Given that the altitude CD has length 6 and segment AD has length 12, find the length of

1. **Problem Statement:** Determine which of the given triangles are right triangles based on their side lengths. 2. **Formula Used:** To check if a triangle is right-angled, use t

1. **Problem Statement:** We have a pair of parallel lines cut by a transversal, creating 8 angles. We will label 6 of these angles and use angle relationships such as correspondin

1. The problem is to find the perimeter of the green triangle with sides 6 cm, 8 cm, and 9 cm. 2. The perimeter of a polygon is the sum of the lengths of all its sides.

1. Bài toán yêu cầu tính độ dài đoạn thẳng $MN$ trong tứ giác $ABCD$ với $M$ và $N$ lần lượt là trung điểm của $AB$ và $CD$. 2. Ta biết $AD=2$, $BC=3$ và $AD$ vuông góc với $BC$.

1. **Problem statement:** Find the distance from point $A(6,3)$ to the vertical line $x=2$. 2. **Formula and explanation:** The distance from a point $(x_0,y_0)$ to a vertical line