📐 geometry

1. **State the problem:** We are given a triangle with sides $a=19$ cm, $c=21$ cm, and the segment $s_{156}=15$ cm (likely a side or segment related to the triangle). We want to so

1. **State the problem:** We have a toy made from a cone and a hemisphere. Both have radius $r$ cm. The slant height of the cone is $3r$ cm. The total surface area of the toy is 30

1. **State the problem:** Find the area of a triangle with sides $b=15$ cm, $c=24$ cm, and angle $\angle A=103^\circ$ between them. 2. **Formula used:** The area $A$ of a triangle

1. **State the problem:** We are given the midpoint $M(6.5, 3.5)$ of segment $\overline{RS}$ and one endpoint $S(15, -12)$. We need to find the coordinates of the other endpoint $R

1. **State the problem:** We are given the midpoint $M(-17, 6.5)$ of segment $\overline{JK}$ and one endpoint $K(-15, -6)$. We need to find the coordinates of the other endpoint $J

1. **State the problem:** We are given the midpoint $M(6.5, 11)$ of segment $\overline{KL}$ and one endpoint $L(13, 16)$. We need to find the coordinates of the other endpoint $K$.

1. **State the problem:** We are given the midpoint $M(2.5, -6.5)$ of segment $\overline{PQ}$ and one endpoint $P(-5, -15)$. We need to find the coordinates of the other endpoint $

1. **Problem 1: Find the length of KL** Given points I, J, K, L on a line with lengths:

1. The problem asks to find the value of each variable $x$ and $y$ given some angles and relationships. 2. From the first part, we have a triangle with angles $60^\circ$, $x$, and

1. **State the problem:** We have a right triangle with hypotenuse $13$, one leg (opposite the $60^\circ$ angle) labeled $a$, the other leg (adjacent to the $60^\circ$ angle) label

1. **State the problem:** We have a right trapezoid with the following known sides and angles:

1. **State the problem:** We have a right triangle with a hypotenuse of length 13, one leg of length $4\sqrt{3}$, and an angle of 60° opposite side $a$. We need to find the lengths

1. **Problem statement:** We have a right triangle with a right angle, a side of length 10 opposite a 60° angle, and another side of length $2\sqrt{3}$. We need to find the lengths

1. **State the problem:** We have a right triangle with a hypotenuse of length 7 inches and one leg of length 4 inches. We need to find the length of the other leg in simplest radi

1. **State the problem:** We have an isosceles triangle with a base of 40 ft and a height of 13 ft. There is a center vertical support beam at the altitude, and two additional vert

1. **State the problem:** Calculate the total surface area of the pyramid with a square base BCDE where each side is 12 cm, and the vertex F is directly above the center M of the b

1. **Problem statement:** Find the measure of angle $\angle C$ in triangle $ABC$ where $\angle B = 55^\circ$, side $AB = 40$, and side $AC = 55$. 2. **Formula and rules:** We use t

1. **Stating the problem:** We have a triangle RBT with a point F on segment RT such that RF is perpendicular to RT and has length 8 cm. Segment RB is labeled as $x$, and segment B

1. **Stating the problem:** We have a pyramid with a vertical height of 25 cm and a base side length of 10 cm. We want to find the apothem (the slant height from the apex to the mi

1. **Problema:** ABCD es un cuadrado con lado 9 cm y dentro está inscrito un círculo que toca todos sus lados. Se pide el área sombreada, que es el área del cuadrado menos el área

1. **Problem statement:** ABCD is a square with side length 9 cm. Inside it, a circle is inscribed touching all sides. Find the shaded area, which is the area of the square minus t