📐 geometry

1. **State the problem:** We need to derive the formula for the area of a triangle using two sides and the sine of the included angle, then apply it to find the area of a triangle

1. The problem asks to draw a 1/4 turn clockwise rotation of a given figure. 2. A 1/4 turn clockwise means rotating the figure 90 degrees in the clockwise direction.

1. **State the problem:** We have a right triangle with one angle measuring 22° and a right angle (90°). We need to find the angle $m$ which is complementary to the 22° angle. 2. *

1. ප්‍රශ්නය: O කේන්ද්‍රය වූ වෘත්තයක A, B, C, D ලක්ෂ්‍ය වෘත්තයේ පිහිටා ඇත. P ස්පර්ශරේඛාව PE හරහා වෘත්තයට ස්පර්ශ කරයි. (i) Â D̂ B = 30° නම් Â Ô B හි ආගය සොවෙන්න.

1. **Problem statement:** Given a right triangle $\triangle ABC$ with right angle at $A$, altitude $AH$ from $A$ to $BC$. Points $I$ and $K$ are the projections of $H$ onto $AC$ an

1. **State the problem:** Find the area of the common region bounded by the circle $$(x-2)^2+(y-2)^2=4$$, the line $$x+y=2$$, and the ellipse $$\frac{x^2}{9}+\frac{y^2}{4}=1$$. 2.

1. The problem is to understand the relationship between faces, vertices, and edges of a polyhedron. 2. According to Euler's formula for polyhedra, the number of vertices $V$, edge

1. Let's start by stating the formulas for the volume of each solid. 2. Volume of a pyramid: The volume $V$ of a pyramid with base area $B$ and height $h$ is given by

1. Let's start by understanding the shape of a cone. A cone has a circular base and a curved surface that tapers to a single point called the apex. 2. Faces: A cone has 2 faces. On

1. 문제를 정리합니다. 길이가 $2a$인 선분 $AB$를 지름으로 하는 반원이 있습니다.

1. Masalani tushuntirish: Teng yonli trapetsiyaning katta asosiga tushirilgan balandlik, katta asosni 6 sm va 18 smli kesmalarga ajratadi. Trapetsiyaning diagonallari o'zaro perpen

1. Masalani tushuntirish: Teng yonli trapetsiyaning o'tmas burchagidan katta asosga tushirilgan balandlik katta asosni 6 sm va 18 sm kesmalarga ajratadi. Trapetsiyaning diagonallar

1. **Problem statement:** Find the areas of the two irregular polygons by splitting them into rectangles. ---

1. **State the problem:** We need to find the radius of a circle given its circumference is 44 cm and $\pi = \frac{22}{7}$. 2. **Recall the formula for circumference:** The circumf

1. The problem is to find the area of a triangle with a base of 10 cm and a height of 6 cm. 2. The formula for the area of a triangle is given by:

1. **State the problem:** We have a large shape made of four trapeziums and one rectangle in the center. The rectangle has dimensions 13 cm by 8 cm. The entire shape has a height o

1. Let's clarify the problem: We want to understand why point E lies on line AGE implies a certain value, here 12. 2. "E lies on AGE" means points A, G, and E are collinear.

1. **State the problem:** We have a triangle ADF with points B, C, D, E, F, and G such that AB = BC = CD and BG = GF. AGE is a straight line, DE has length $x$, and EF has length 1

1. **State the problem:** We are given a circle with center $P$ and two diameters $\overline{BD}$ and $\overline{AC}$. We need to find the measure of the major arc $\overset{\frown

1. **State the problem:** We need to find the measure of the minor arc $\widehat{AE}$ in degrees in a circle with center $P$ where $\overline{BD}$ and $\overline{EC}$ are diameters

1. **State the problem:** We have a triangular prism with given side lengths: EF = 21 mm, FC = 6 mm, and DC = 17 mm. We need to find: a) The length of segment AF.