📐 geometry

1. **State the problem:** We need to find the surface area of wrapping paper required to cover a present with dimensions 6 in. long, 5 in. wide, and 3.5 in. tall. 2. **Formula used

1. **State the problem:** We need to find the surface area of a hemisphere with radius $r=57$ meters, including the circular base. 2. **Formula used:** The surface area $A$ of a he

1. The problem asks for the exponent used to express the volume of a cube with edge length 21 cm. 2. The formula for the volume $V$ of a cube with edge length $a$ is:

1. **Problem statement:** We are given a triangle QRP with points R, S, and P on a straight line (RSP). The angle \(\angle QSP = 80^\circ\) and line QS is perpendicular to RS. We n

1. **Problem statement:** We have a 30-60-90 right triangle. The altitude to the hypotenuse is divided into two segments of lengths $x$ and $y$ by the median to the hypotenuse. We

1. **Problem Statement:** We have three polygons: an equilateral triangle, a rhombus with a 60° angle, and a regular hexagon. Each contains mutually tangent congruent disks. We den

1. **Problem Statement:** Calculate the area of each triangle and trapezoid given their dimensions. 2. **Formula for Area of Triangle:**

1. **State the problem:** We have two rectangles with the same perimeter. The green rectangle has width 11 mm and height 18 mm. The orange rectangle has height 4 mm and an unknown

1. **State the problem:** We have two rectangles with the same perimeter. One rectangle has dimensions 14 ft by 2 ft, and the other is a purple square with side length 7 ft. We nee

1. **State the problem:** We have two rectangles with the same perimeter. The first rectangle has sides 19 km and 17 km. The second rectangle has one side 15 km and the other side

1. **State the problem:** We need to find the perimeter of a sector of a circle where the arc length is 21 cm and the central angle is 120 degrees. 2. **Recall the formula for the

1. **Problem Statement:** We need to find the scale factor to reproduce a blueprint so that its area becomes 45 square inches and it fits on a standard sheet of paper. 2. **Underst

1. **Problem Statement:** (a) Find the size of angle $\angle ACB$ in triangle $ABC$ where $BC=AC=7$ cm.

1. The problem asks to find the bearing of Liverpool from London given the bearing of London from Liverpool is 130°. 2. Bearings are measured clockwise from the north direction. Th

1. **Problem Statement:** We have several geometry problems involving triangles and polygons with given side lengths and angles. We will solve for areas, side lengths, and angles s

1. **Problem Statement:** Given a diagram with two parallel lines cut by a transversal, find the unknown angles $x$, $y$, and $z$ using properties of corresponding angles, interior

1. **State the problem:** We need to find the measure of angle $\angle GMK$ given two expressions for angles formed by parallel lines and a transversal. 2. **Identify the angles:**

1. **Problem Statement:** We need to find the measure of angle $\angle GMK$ given two expressions for angles related by parallel lines and a transversal. 2. **Given:**

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \((2x + 122)^\circ\) and \((154 - 2x)^\circ\). We need to

1. **State the problem:** We need to find the measure of angle $\angle MON$ given two algebraic expressions for angles formed by intersecting lines. 2. **Identify the angles:** The

1. **Problem Statement:** We need to find the measure of angle $\angle QWU$ given two angles formed by a transversal crossing two parallel lines: one angle at point $V$ is $(100 -