📐 geometry

1. **State the problem:** We need to find the total paper area required to make one hollow square pyramid tree, including the base. 2. **Given:**

1. **State the problem:** We need to find the amount of reflective material required to cover a rectangular prism with dimensions length $1.3$ m, width $0.8$ m, and height $1.1$ m.

1. **State the problem:** We need to find the total surface area of a triangular prism tent, including the floor, to determine how much material Dmitri's mom will need. 2. **Identi

1. **Problem statement:** Amir wants to find the surface area of a square pyramid roof with a base side length of $0.4$ meters and a triangular face height of $0.6$ meters. The sur

1. **State the problem:** Jordan needs to find the total surface area of a rectangular prism with length 10 cm, width 10 cm, and height 90 cm to cover it with carpet. 2. **Formula

1. **Problem statement:** Find the unknown angles in each quadrilateral or polygon given the known angles. 2. **Key formula:** The sum of interior angles of a quadrilateral is $$36

1. **Problem Statement:** Find the measures of the given angles and segments in triangles ΔABC and ΔJKL where G and P are incenters respectively.

1. **Énoncé du problème :** Nous avons plusieurs questions liées à des figures géométriques avec des segments et des parallélismes à démontrer, ainsi que des calculs de distances e

1. **Problem Statement:** Given a circle with center $O$ and points $A$, $B$, and $C$ on the circumference, the angle $\angle AOB = 72^\circ$. We need to find the angles $\angle OA

1. **Problem Statement:** We have two isosceles triangles, ABC and DEF. In triangle ABC, sides AB and AC are equal, and side BC is labeled as $(x - 4)$. In triangle DEF, sides DF a

1. **State the problem:** We have a right-angled triangle with a base of 9.1 cm and an area of 23.66 cm². We need to find the size of angle $y$, which is opposite the base. 2. **Re

1. **State the problem:** We need to find the volume of a cylinder with radius $r=7$ cm and height $h=15$ cm. 2. **Formula for the volume of a cylinder:**

1. Problem 45: Given secants FA and EA intersecting outside the circle at A, with FA = 24 cm, LA = 10 cm, and MA = 12 cm, find EA. 2. Use the secant-secant power theorem: If two se

1. **State the problem:** We are given two triangles, \(\triangle PST\) and \(\triangle RTU\), with some angles and sides marked congruent. We need to prove the triangles are congr

1. समस्या को समझें: त्रिभुज ABC में, P एक समद्विभाजक बिंदु है जो कोण B और कोण C को विभाजित करता है। दिया गया है कि BC ∥ LM और LM = BL + CM है। हमें यह सिद्ध करना है कि BC ∥ LM। 2.

1. The problem states that RS is the diameter of a circle with center O, and we need to find the value of angle $y$ at point S on the circumference. 2. Important fact: The angle su

1. **State the problem:** We need to find the area of the shaded shape WXZY, which is the area between two circular sectors OWX and OYZ with the same central angle of 75° but diffe

1. **State the problem:** We have a sector OAB of a circle with radius $r = 5.9$ mm and area $28$ mm². We need to find the central angle $\theta$ in degrees to 1 decimal place. 2.

1. **Problem 12:** Given $m\angle ABC = 35^\circ$, $m\angle BAC = 29^\circ$, and $\angle ACB \cong \angle DEB$, find $m\angle DEB$. 2. Since $\triangle ABC$ is a triangle, the sum

1. **State the problem:** We are given two triangles ABC and DEF with some angles and side lengths. We need to determine if they are similar and, if possible, find the unknown side

1. **Stating the problem:** We are given two triangles, ABC and DEF, with angles $A=63^\circ$, $B=48^\circ$, $E=89^\circ$, and $F=48^\circ$. We want to find the missing angles $C$