📐 geometry

1. The problem states that triangle ABD is isosceles with AB = AD. 2. Given angles are \(\angle D = 74^\circ\) and \(\angle C = 28^\circ\). \(\angle B\) is marked as \(x\), and ang

1. **Stating the problem:** We have an isosceles triangle ABD with equal sides AB = AD. 2. Since AB = AD, the angles opposite these sides are equal. These are angles at B and D.

1. **State the problem:** We have a right triangle with legs 8 cm and 15 cm. Inside the triangle on the hypotenuse, two squares are drawn, one with an area of 9 cm², and the other

1. **State the problem:** We are given six different figures with three parallel lines labeled $l$, $m$, and $n$, intersected by two transversals. We need to find the unknown value

1. The problem describes a 3-D shape with 5 faces. 2. Two opposite faces are triangles — these are the bases.

1. The problem asks for the volume of a cylinder with radius $r=5$ cm and height $h=8$ cm. 2. The formula for the volume of a cylinder is $$V=\pi r^2 h$$.

1. **State the problem:** Each interior angle of a regular polygon measures 160°. We need to find the number of sides of this polygon. 2. **Recall the formula for the interior angl

1. **Problem:** A rectangular field with length 5 m and width 8 m has a cement path 2 m wide around it. Find the area of the cement path. 2. **Step 1:** Calculate the dimensions of

1. **Problem statement:** (a) Find the distance in cm between two stadiums on Map B whose scale is 1:5000 given the distance on Map A (scale 1:2000) is 12.5 cm.

1. **Problem:** Find the area of the cement path around a rectangular field of length 5 m and width 8 m with a 2 m wide cement path around it. Step 1: Find the total length and wid

1. **Problem statement:** Calculate perimeter and area of various shapes, volumes, and paint coverage as described. 2. Circle with diameter 23 feet:

1. **Stating the problem:** We have two questions. - First, to find the equation representing the line of reflection for the given graph, which involves polygons reflected across a

1. **সমস্যাটি বর্ণনা:** একটি সমমিতিচতুভুজ ABCDEF যার প্রতি বাহুর দৈর্ঘ্য 4 সেমি। প্রশ্নগুলোর উত্তর পাওয়ার জন্য গাণিতিক উপায় দেখানো হয়েছে। 2. **প্রশ্ন ২৫:** ABCDEF এর ক্ষেত্রফল ব

1. Bài toán yêu cầu tính thể tích $V_b$ của hình đã cho. 2. Để tính thể tích $V_b$, ta cần xác định công thức thể tích phù hợp với hình dạng của hình (ví dụ: hình hộp chữ nhật, hìn

1. The problem asks to create a 3D image, but no mathematical function or equation has been provided. 2. To generate a 3D plot, we need a mathematical expression typically involvin

1. The problem presents a set of 12 different geometric figures described by vertices' labels and numbers at corners or edges. 2. The figures include triangles with numbers at vert

1. **State the problem:** Given a circle with center O and points P, Q, R, S, T on its circumference, with line TOQ straight and T on PS, and PQ = QR, find: - (8.2.1) angle $\hat{P

1. **State the problem:** We have a ray of light passing through point $P(2, 3)$, reflecting on the x-axis at point $A$, and the reflected ray passes through point $Q(5, 4)$. Point

1. Stating the problem: We need to find the volume of a pentagonal pyramid given the base length $b = 11$ cm, apothem $a = 7.57$ cm, and height $h = 16$ m. 2. Convert height to cm

1. **State the problem:** We have a 50-dimensional hypercube with side length 1. The boundary is defined by points where at least one coordinate $x_j$ lies in either $[0,0.05]$ or

1. **State the problem:** We have a $50$-dimensional hypercube with side length $1$. The boundary is defined as points where at least one coordinate $x_j$ is in $[0,0.05]$ or $[0.9