📐 geometry

1. **State the problem:** We are given a triangle with angles expressed as algebraic expressions: $5x - 11$, $2x + 20$, and $11x - 63$. We need to solve for $x$ and then find the m

1. **Problem Statement:** Calculate the surface area of a triangular pyramid with given edge lengths: 12 cm, 8 cm, 6.9 cm, and 8 cm.

1. **State the problem:** We need to find the area of triangle $\triangle ABC$ with sides $AB=44$ km, $BC=48$ km, and $AC=39$ km using Heron's formula. 2. **Heron's formula:** The

1. Given $m \angle 2 = 50$, we need to find $m \angle 3$. 2. From the diagram, $\angle 2$ and $\angle 3$ are vertical angles, which means they are equal.

1. The problem asks to name the pairs of congruent and adjacent sides in a kite. 2. In a kite, two pairs of adjacent sides are congruent. This means each pair shares a common verte

1. **State the problem:** We are given a circle with center O and two arcs: $m\angle JR = 65.1^\circ$ and $m\angle FL = 21.4^\circ$. We need to find the measure of the exterior ang

1. **بيان المسألة:** لدينا ثلاث نقاط A، B، C ليست في استقامة.

1. **State the problem:** We are given a circle with center A and points L, B, Q, G, and M on or around the circle. We know the measures of angles $\angle MLG = 20.45^\circ$ and $\

1. **Problem Statement:** Determine the length of cylinder CB in the given mechanical diagram where angles are 90°, 25°, and 55°. 2. **Understanding the problem:** The points A, C,

1. **Problem:** Find the area of the L-shaped polygon with sides 18 m, 25 m, 5 m, and 30 m. 2. **Formula and approach:** To find the area of an L-shaped polygon, we can divide it i

1. The problem asks for the area of Amanda's living room carpet, which is a rectangle with length 16 feet and width 13 feet. 2. The formula for the area $A$ of a rectangle is:

1. **State the problem:** We need to find the area of Megan's backyard that is NOT covered by the pool. 2. **Identify the shapes and dimensions:**

1. **State the problem:** We need to find the volume of a cylindrical grain silo with diameter 16 ft and height 47 ft. 2. **Formula for volume of a cylinder:**

1. **Problem statement:** Given triangle OPQ with points R on OQ and S on PQ such that segment RS is parallel to segment OP. We know $OP=5.6$, $RQ=4.8$, and $OR=3.6$. We need to fi

1. **Problem Statement:** We are given two triangles sharing a vertex with sides labeled 4 and 12 on the left triangle, and 2 and 6 on the right triangle. We need to determine whic

1. **State the problem:** We need to find the area of the blue shaded region inside a large rectangle of height 20 cm and width 10 cm, where a right triangle with one leg 8 cm is f

1. **State the problem:** We need to determine which shortcut can be used to prove that the two triangles shown are similar. 2. **Given information:** The two triangles share a com

1. The problem states that the net of a cube is shown on the coordinate plane, and we need to find the surface area of the cube in square units. 2. A cube has 6 faces, all of which

1. **State the problem:** Find the measure of angle $\angle ADC$ in a quadrilateral $ABCD$ inscribed in circle $P$, given $\angle BAD = 110^\circ$ and $\angle ABC = 72^\circ$.

1. The problem is to calculate the bearing, which typically refers to the direction or angle from a reference point, often north, to another point or object. 2. Bearings are usuall

1. **State the problem:** We are given two adjacent angles on a straight line, $3x$ degrees and $(8x + 70)$ degrees, and we want to verify if the equation $3x + (8x + 70) = 180$ is