📐 geometry

1. **State the problem:** We are given three points $N(-3,1)$, $O(-3,-7)$, and $P(1,-5)$ that form a triangle. We need to find the perimeter of this triangle. 2. **Recall the formu

1. **Stating the problem:** We need to find the area of rectangles using the formula $$A = r \times b$$ where $r$ and $b$ are the lengths of the sides.

1. **State the problem:** Find the area of rectangles using the formula $$A = l \times b$$ and find the actual area when $$l=3$$ cm and $$b=1$$ cm.

1. **State the problem:** We have a right-angled triangle with adjacent sides of lengths $x$ cm and $(x-1)$ cm, and the hypotenuse length is $\sqrt{13}$ cm. We need to find the val

1. **Énoncé du problème :** Soit le triangle EFG avec EF = 5 cm, EG = 4 cm, FG = 3 cm. Le point M est sur le segment [EG] tel que EM = 6 cm. Une droite parallèle à (FG) passant par

1. **Énoncé du problème :** Calculer EN et MN dans le triangle EFG où EF = 5 cm, EG = 4 cm, FG = 3 cm, M est un point sur [EG] tel que EM = 6 cm, et la droite passant par M et para

1. **Énoncé du problème :** Calculer les longueurs EN et MN dans le triangle EFG où EF = 5 cm, EG = 4 cm, FG = 3 cm, et M est un point sur [EG] tel que EM = 6 cm. Une droite parall

1. **State the problem:** We have a circle with center $O$ and diameter $FG$. The arc $FXG$ has length $14\pi$. We need to find the length of the line segment $XO$. 2. **Understand

1. **Stating the problem:** We are given a geometric figure with points V, A, B, C, M, N, X, and Y.

1. **State the problem:** We are given the circumference of a plastic pipe as $4 \frac{1}{2}$ inches and the pipe thickness as $\frac{1}{16}$ inch. We need to find the inside diame

1. **State the problem:** A customer gives the circumference of a tire's wheel rim as 44 inches. We need to find the approximate diameter of the tire.

1. **State the problem:** We have an L-shaped building drawn to scale where 1 cm on the drawing represents 75 m in reality. The sides of the building on the drawing are 7 cm, 6 cm,

1. **Problem Statement:** We need to find all segments that are two-thirds the length of $\overline{AG}$. 2. **Understanding the setup:** There are five congruent circles arranged

1. The problem asks to find all segments on line AF that are exactly two-fifths the length of AF. 2. Since points A, B, C, D, E, F lie on AF, the length AF is divided into segments

1. **State the problem:** We need to find the total volume of 8 hemisphere-shaped portions of ice cream, each with a diameter of 6 cm.

1. **State the problem:** Find the surface area of a rectangular prism with height $5$ inches, width $6$ inches, and length $9$ inches. 2. **Formula for surface area of a rectangul

1. **State the problem:** We need to find the surface area of a cube with edge length 8 yards. 2. **Formula:** The surface area $S$ of a cube with edge length $a$ is given by

1. **State the problem:** We need to find the value of $x$ in a triangle where the three angles are given as $(63 + x)^\circ$, $(183 - x)^\circ$, and $2x^\circ$. 2. **Recall the tr

1. **State the problem:** We have a convex pentagon with interior angles 82°, 129°, 121°, 147°, and an unknown angle $x$. We need to find $x$. 2. **Formula for sum of interior angl

1. **State the problem:** You want to find the length of one side of a rectangle when you know the area and the length of the other side. 2. **Formula:** The area $A$ of a rectangl

1. **State the problem:** Determine the relationship between angles $\angle 7$ and $\angle 3$ formed by two parallel lines intersected by two transversals. 2. **Recall relevant the