📐 geometry

1. The problem asks for the measure of angle $\angle B$ in the hexagon with given interior angles: $\angle A = 120^\circ$, $\angle B = 129^\circ$, $\angle C = 148^\circ$, $\angle D

1. **Problem statement:** Find the value of $x$ in triangle $ABC$ where angles are $x^\circ$ at $A$, $2x^\circ$ at $B$, and $330^\circ$ at $C$. 2. **Formula used:** The sum of inte

1. The problem asks to identify the type of special triangle given one angle of 30° and a right angle (90°). 2. A triangle with angles 30°, 60°, and 90° is a well-known special rig

1. **Problem statement:** We have a right triangle with a hypotenuse $e$, one leg of length $3\sqrt{3}$, and an angle of $60^\circ$ adjacent to that leg. We want to find the length

1. **Problem statement:** We have two similar rhombuses ABCD and ECFA. The diagonals EF and BD measure 4 m and 16 m respectively. We need to find the perimeter of the larger rhombu

1. **State the problem:** We need to find the total volume of wax required to make 110 cylindrical candles, each with diameter 6 inches and height 6 inches. 2. **Formula for the vo

1. **Problem statement:** A cube has a volume of 216 cm³. We need to find:

1. **State the problem:** We are given a right rectangular prism with three face areas: front face area = 39 cm², top face area = 65 cm², and side face area = 15 cm². We need to fi

1. **Stating the problem:** We are given a rectangular prism with dimensions 6 cm, 7 cm, and 12 cm. We want to calculate its volume and surface area.

1. **Problem statement:** A fish pond is a rectangular prism with length 4 m, width 3 m, and depth 2 m.

1. **State the problem:** We have an equilateral triangle $\triangle ABC$ with side length 5 cm.

1. The problem asks if the two triangles can be proved congruent and which postulate can be used. 2. The common triangle congruence postulates are:

1. **Problem statement:** We have a square divided into 4 parts: triangles A and B, and trapeziums C and D. Given:

1. **Stating the problem:** We are given angles $x^\circ$, $w^\circ$, $y^\circ$ with the condition $BA = BD$ and the ratio $x : y = 2 : 1$. We need to find the relationship between

1. The problem asks for the surface area of a right rectangular prism with dimensions 3 cm (height), 10 cm (width), and 11 cm (depth). 2. The formula for the surface area $A$ of a

1. **Problem Statement:** Find the surface area of the first cuboid with dimensions 4 cm by 4 cm by 7 cm. 2. **Formula:** The surface area $A$ of a cuboid with length $l$, width $w

1. **Problem:** Find the surface area of the first cuboid with length $8$ cm, width $5$ cm, and height $5$ cm. 2. **Formula:** The surface area $A$ of a cuboid is given by:

1. **Problem statement:** We have two circles with radii $a$ and $b$, and the distance between their centers is $c$. We want to find the area of their overlapping region. 2. **Form

1. **Problem statement:** We have two circles with radii $a$ and $b$ where $a > b$, and the distance between their centers is $c$. We want to find the area of their overlap. 2. **K

1. **Problem statement:** Find the percentage of the 7 by 7 grid that is shaded. 2. **Total squares:** The grid has $7 \times 7 = 49$ squares.

1. **State the problem:** We have a right-angled triangle XYZ with right angle at Y. 2. **Given:**