📐 geometry

1. **State the problem:** Find the area of a circle with radius 9 yd using $\pi = 3.14$ without rounding the answer. 2. **Formula for area of a circle:**

1. The problem asks for the sum of the interior angle measures of a convex 18-gon, which is a polygon with 18 sides. 2. The formula to find the sum of interior angles of a polygon

1. **Problem statement:** Given a quadrilateral ABCD, decompose it into triangles by drawing segments from vertex A to all non-adjacent vertices. 2. **Decomposition:** The non-adja

1. **Problem statement:** We have three similar triangles with given angles and side lengths. We need to find the values of $w$, $x$, and $y$. 2. **Recall properties of similar tri

1. **Problem statement:** Given the rectangle PQRS with vertices P, Q, R, S, find the image points P', Q', R', S' after the transformation (x, y) \to (2x, y). 2. **Transformation f

1. **Understanding Similarity:** Similarity in geometry means two shapes have the same shape but not necessarily the same size. 2. **Key Properties of Similar Figures:** Correspond

1. **Stating the problem:** Explain the concept of "chevauchements" (overlaps) in a mathematical or geometric context. 2. **Definition:** "Chevauchements" means overlaps or interse

1. **Stating the problem:** Find the surface area of a triangular prism. 2. **What is a triangular prism?** It is a 3D shape with two triangular bases and three rectangular faces c

1. **Stating the problem:** You want to understand everything about surface area to pass your exam. 2. **What is surface area?** Surface area is the total area that the surface of

1. **Stating the problem:** We have a trapezoid ABCD with parallel sides AD and BC. Given are side AD = 5 cm, side AB = 12 cm, and the height (perpendicular distance from C to AB)

1. **State the problem:** Find the area of the kite with diagonals of lengths 1 and 2. 2. **Formula for the area of a kite:** The area $A$ of a kite is given by

1. The problem is to find the volume of a rectangular prism (in this case, a cube) with edge lengths of 5.1 inches each. 2. The formula for the volume $V$ of a rectangular prism is

1. **State the problem:** We are given a rectangular prism with length $9$ inches, width $5$ inches, and an unknown height. We need to find the height given the volume or find the

1. **Problem statement:** Given points A, B, C, A', B', C' on concurrent lines 𝓛, 𝓜, 𝓝 meeting at O, with AB \parallel A'B' and BC \parallel B'C', prove using Thales theorem that $

1. **Problem statement:** Given an isosceles triangle $\triangle ABC$ with $|AB| = |AC|$, and $M$ as the midpoint of $BC$, prove that the median $AM$ bisects the angle $\angle A$ a

1. **State the problem:** We have a semicircle with diameter $BC = 16$ cm and a triangle $ABC$ inside it. The angle at $A$ is $0.68$ radians. We need to find the area of the shaded

1. **Problem Statement:** Deduce that the diagonals of a rhombus meet at right angles. 2. **Definition and Properties:** A rhombus is a parallelogram with all sides equal in length

1. The problem is to show the image of a labeled parallelogram. 2. Since this is a request for an image and not a mathematical problem, I cannot provide a mathematical solution or

1. **Problem Statement:** Given a parallelogram with its two diagonals intersecting, find the pairs of congruent triangles using the parallelogram side theorem and ASA (Angle-Side-

1. **Problem statement:** Calculate the area of the shaded border region around a smaller rectangle inside a larger rectangle.

1. **Problem statement:** Show by induction that the angle sum of a convex $n$-gon is $$(n-2)\pi$$ for integer $n \geq 3$.