📐 geometry

1. **Problem Statement:** In triangle $\triangle ABC$, $DB$ and $AE$ are medians. Given: - $BE = 6y + 10$

1. **Problem statement:** Two cubes each with edge length 6 cm are joined end to end. We need to find the surface area of the resulting cuboid. 2. **Understanding the problem:** Ea

1. **Problem statement:** Given triangle ABC with sides AB = 7.2 cm, AC = 3.5 cm, and angle BAC = 28°, find the measure of angle ACB to the nearest degree. 2. **Formula used:** We

1. **Stating the problem:** We have triangle ABC with sides AB = 7.2 cm, AC = 3.5 cm, and angle BAC = 28°. We need to find the measure of angle ACB.

1. **State the problem:** We have a triangle with a base of 7 cm and two angles adjacent to the base: 40° and 20°. We need to find the length $x$ of the side opposite the base. 2.

1. **Problem b:** Find $x$ given angles $95^\circ$ and $125^\circ$ around a point. 2. **Step 1:** Recall that the sum of angles around a point is $360^\circ$.

1. **Problem Statement:** We are given a circle with points A, B, C, D on its circumference and angles marked as follows: \(\angle A = 55^\circ\) (right angle), \(\angle B = 39^\ci

1. **State the problem:** Find the volume of a right triangular prism where the base is a right triangle with one leg 5.7 cm, an adjacent angle of 42°, and the prism height (length

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