📐 geometry

1. **State the problem:** We have a map scale of 1:100,000, meaning 1 cm on the map represents 100,000 cm in reality. 2. **Formula and explanation:** The real distance $D$ is given

1. The problem is to find unknown angles in various polygons: triangle, square, rhombus, kite, and quadrilateral. 2. Important formulas and rules:

1. **Problem Statement:** Find the measures of angles (a) $\angle ADX$, (b) $\angle ABC$, and (c) $\angle BCD$ given the circle with points $A$, $B$, $C$ on the circumference, poin

1. **State the problem:** We are given that the sum of the interior angles of a regular polygon is 1440 degrees. We need to find the size of each exterior angle of this polygon. 2.

1. The problem is to understand and apply the circle theorem. 2. One common circle theorem states: "The angle subtended by a diameter at the circumference is a right angle."

1. **Problem statement:** Given a right-angled triangle with an angle $\Omega = 55^\circ$ and a circle of diameter $D = 20$ mm inscribed such that it is tangent to the hypotenuse a

1. **Problem statement:** Given a circle with tangent segments VQ and VK, and a line segment IK, where $QV=8$ cm, $IK=24$ cm, and $KV=x$ cm, find the value of $x$. 2. **Key propert

1. **Problem statement:** Four congruent rectangles are arranged to form an inner square of area $20$ cm² and an outer square of area $64$ cm². We need to find the perimeter of one

1. **Problem statement:** The shape is a rectangle with a notch on top. The total perimeter is 60 cm. The rectangle's height is 8 cm, the bottom length is 18 cm, and the notch widt

1. **Problem Statement:** Meg is playing with a toy shaped like a hexagonal prism divided into six triangular faces. Three alternate triangular faces are shaded, each with a white

1. **Stating the problem:** Encik Hamid wants to plant 18 oil palm trees arranged so that the distance between each tree is 9 m, and the planting pattern forms an equilateral trian

1. **State the problem:** Find the area of the irregular polygon composed of three rectangles stacked like steps, with all sides meeting at right angles. 2. **Identify the shapes a

1. **Problem statement:** Find the total surface area of a right pyramid VABCD with a rectangular base of length 16 cm and width 14 cm, and slant edge length 25 cm. 2. **Formula an

1. **Problem statement:** (a) Find the height of pyramid VPQR inside the frustum.

1. The problem is to verify or understand why the answer is 1155 square meters. 2. Typically, such a problem involves finding the area of a shape, often a rectangle or composite fi

1. **Problem statement:** Find the total surface area of a building with a floor plan shaped like an irregular polygon (a "U" shape) and a flat roof. The building height is 8 m. 2.

1. **State the problem:** We need to find the total surface area of a building that is 8m tall, with a floor plan shaped like a large rectangle with a smaller rectangular cutout at

1. Énoncé du problème : On a un triangle ABC avec E sur AB et F sur AC, et BC parallèle à EF.

1. **State the problem:** We have an isosceles triangle PQR with base RQ = 22 cm and height from P to midpoint M of RQ equal to 10 cm. We need to find the length of side PR. 2. **R

1. **State the problem:** Kayden has 50 m of railing but needs to know how much more railing is required to go all the way around the roof garden, which has a composite shape with

1. **State the problem:** We have a rectangular pyramid with base ABCD where AB = 7 cm and BC = 9 cm. The apex is T, and all edges TA, TB, TC, and TD are 12 cm. M is the midpoint o