📐 geometry

1. **Problem Statement:** Given circle C with points A, B, D, E, F on the circumference and diameter BE, and angles $m\angle EA = 75^\circ$, $m\angle AD = 68^\circ$, and $m\angle D

1. The problem states: In any triangle, the _______ of the hypotenuse is equal to the sum of the ______ of the other two sides. 2. This is a classic property of right triangles kno

1. **Problem:** A rectangular box with base dimensions 2 inches by 6 inches and height 10 inches holds 12 ounces of cereal. The manufacturer wants a new box with base 3 inches by 5

1. **Énoncé du problème :** Soient ABC un triangle avec les points pondérés G = bar{(A; -1), (B; -4), (C; 3)}, I barycentre de (B; -4) et (C; 3), K barycentre de (B; -4) et (A; -1)

1. **Problem Statement:** We are given a pentagon ABCDE with right angles at vertices B, D, and E. The lengths AE = AB = 5, BC = 12, and DC = DE. We need to find the area of pentag

1. **Problem Statement:** We are given a pentagon ABCDE with the following conditions: $AE = AB = 5$, $BC = 12$, and $DC = DE$. The angles at vertices B, D, and E are right angles.

1. **Problem Statement:** Find the area of trapezoid PQST with bases $TS=12$ and $PR=24$, and legs $PT=10$ and $SR=10$. 2. **Formula for area of trapezoid:**

1. **State the problem:** We need to find the arc length of a circle with radius $9$ m and a central angle of $25^\circ$. 2. **Formula:** The arc length $s$ of a circle is given by

1. **Problem statement:** Find the area of the shaded region inside a rectangle of dimensions 12 cm by 6 cm, excluding a circle of radius 2 cm inside it. 2. **Formula used:**

1. **Problem statement:** Given a right triangle ABC, the altitude relative to the hypotenuse divides it into two segments measuring 3.6 cm and 6.4 cm. Find the lengths of the legs

1. **State the problem:** We need to find the value of the angle $x$ in a regular decagon (10-sided polygon) where $x$ is an interior angle formed by two triangles inside the decag

1. **Problem statement:** Find the value of $1 - 20 = \text{?}$ with options involving angles $30^\circ$, $90^\circ$, $60^\circ$. Since the problem is unclear as written, we move t

1. **Problem (a):** Find the area of grass in a rectangular park measuring 50m by 40m with a 3m flower bed around two longer sides and one short side, and a circular fish pond of d

1. **Problem (a):** A rectangular park measures 50m by 40m. A 3m flower bed is made around the two longer sides and one short side. A circular fish pond of diameter 8.0m is constru

1. Problem (a): Find the area of grass in a rectangular park 50m by 40m with a 3m flower bed around two longer sides and one short side, and a circular fish pond of diameter 8m in

1. **State the problem:** Calculate the total area of a composite shape consisting of a rectangle, a triangle, and a circle arranged as described.

1. **Problem statement:** We have triangle PQR with vertices P(3,2), Q(-1,1), and R(-3,-1).

1. **Problem Statement:** (a) A rectangular park measures 50m by 40m. A 3m flower bed is made around the two longer sides and one short side. A circular fish pond of diameter 8.0m

1. Задатак: Дати су лопта полупречника $R$ и раван која садржи крајњу тачку полупречника лопте и гради угао од 60° са тим полупречником. Потребно је одредити површину пресека лопте

1. The problem is to understand and simplify the expression $\frac{\theta}{360} \times \pi r^2$. 2. This formula calculates the area of a sector of a circle, where $\theta$ is the

1. The problem is to find the unknown side or angle in a triangle, but since no specific triangle details are given, let's assume you want to solve for a side using the Pythagorean