📐 geometry

1. The problem is to understand and simplify the expression $$D^2 = (4k)^2 + (3k)^2$$ and explain where the variable $k$ comes from. 2. This expression looks like the Pythagorean t

1. **State the problem:** We have triangle SWU with side SW = 45. Inside it, segment UV is parallel to SW and proportional. Given segments WV = 16 and TV = 15, we need to find the

1. **State the problem:** We have two similar triangles sharing vertex S. We know side lengths 45, 15, and 16, and we need to find the missing side length $UV$ in the smaller trian

1. **State the problem:** Find the length and midpoint of the line segment with endpoints $(-2, 6)$ and $(4, 0)$. 2. **Length formula:** The length $d$ between two points $(x_1, y_

1. **State the problem:** We have a polygon with an area of 129 cm² and some given side lengths, including an unknown length $x$. We need to find $x$. 2. **Analyze the shape:** The

1. **Problem statement:** Graph a circle with center at $(1,0)$ that passes through $(-3,0)$. Find the area and circumference of the circle, both in terms of $\pi$ and to the neare

1. The problem: Construct a triangle given the base length and the two adjacent angles. 2. Given: Base $AB = 8$ cm, angle $A = 50^\circ$, angle $B = 60^\circ$.

1. **Problem statement:** Prove that $\hat{A}BD = \hat{A}CE$ using the given figure with triangle $ABC$ and points $D$ and $E$ on the line through $B$ and $C$. 2. **Key idea:** Ang

1. The problem is to understand why the aspect ratio is 4:3. 2. Aspect ratio is the ratio of width to height of an image or screen.

1. **Problem 12:** For a 200" diagonal image with a display resolution of 1024 x 768 pixels, find the screen coordinates of points located on the LCD screen. 2. **Step 1:** Underst

1. সমস্যাটি হলো: একটি কোণকে ডিগ্রি (D°) এবং রেডিয়ান (R) পদ্ধতিতে প্রকাশ করা হলে, প্রমাণ করতে হবে যে $$\frac{D}{180} = \frac{R}{\pi}$$। 2. কোণ পরিমাপের মূল সূত্র হলো: ১ পূর্ণ বৃত্ত

1. **Problem 4: Find the area of the L-shaped polygon with external dimensions 8 cm by 12 cm and an internal cut of 4 cm by 4 cm.** 2. The formula for the area of a rectangle is $\

1. **Problem Statement:** We have 6 LEDs placed evenly around a circle of radius 100 inches centered at the origin (0,0). The LEDs are at angles 0°, 60°, 120°, 180°, 240°, and 300°

1. **State the problem:** Calculate the surface area of a square pyramid with base side length $6$ cm and slant height $7$ cm. 2. **Formula used:** The total surface area $A$ of a

1. **State the problem:** Find the area of a parallelogram with base length $2.6$ inches and height $2$ inches. 2. **Formula:** The area $A$ of a parallelogram is given by the form

1. **State the problem:** Find the area of a parallelogram with base $6$ cm and height $4$ cm. 2. **Formula:** The area $A$ of a parallelogram is given by:

1. **State the problem:** We have two triangles ABC and CDE sharing point C, with points A, C, D collinear and points B, C, E collinear. Given lengths AC = 24 cm, BC = 31 cm, CE =

1. Stating the problem: We need to find the formulas for surface area and volume for each of the six given shapes composed of cylinders and cones with given height and radius param

1. **Problem statement:** Given a right triangle XYZ with right angle at Y, altitude YW to hypotenuse XZ, and segments XW = r, WZ = s, find the altitude $h$. 2. **Formula used:** I

1. **Problem statement:** - Question 6: In triangle KLM, KM = 6 cm and angle KLM = 30°. Find the length of KL.

1. **Problem Statement:** Construct a triangle \(\triangle ABC\) such that \(AB = 6\) cm, \(BC = 4\) cm, and \(CA = 5.5\) cm. 2. **Formula and Rules:** To construct a triangle give