📐 geometry

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

1. **State the problem:** We have a right triangle with two 45° angles, meaning it is an isosceles right triangle (45°-45°-90° triangle). The hypotenuse is given as $7\sqrt{3}$, an

1. **Problem statement:** Given a circle with center O, tangent FE at point E, and points D and G on the circle such that EG = GF. Angle FÊG is $x$. We need to:

1. The problem is to find the area of a right triangle with legs measuring 8.9 cm and 8.1 cm. 2. The formula for the area of a right triangle is:

1. **Problem statement:** Calculate the angles:

1. نبدأ ببيان المسألة: لدينا مثلث به نقاط D و E و F و G و H، معطى أن DE = 8 سم، EH = 2 سم، EF = 6 سم، FG = 10 سم، والزوايا عند H و G قائمة. 2. المطلوب هو حساب النسبة (EF) // (HG) أ

1. Задачата: Имаме правоаголник ABCD каде што BC=2\cdot AB. Точката P е на страната AD така што AD=BP. Треба да најдеме големината на аголот \angle CPD. 2. Запишуваме што знаеме: В

1. **Problem Statement:** We need to determine which additional information is sufficient to prove that triangle $ABC$ is congruent to triangle $EBD$ given that lines $m$ and $n$ a

1. **State the problem:** We have a right square pyramid with a total surface area of $100 + 20\sqrt{146}$ square inches, including a base area of 100 square inches. We need to fin

1. **State the problem:** We have a board 104 inches long resting on a brace 22.5 inches high and 63 inches from the base of the board on the ground. We want to find how high the t