📐 geometry

1. **State the problem:** We have a triangle RST with sides RS = $3x + 4$ and RT = $8x + 4$. The angle between the extension of JR and RT is 140°. We want to find the value of $x$.

1. **State the problem:** We need to find the surface area of a right rectangular prism with dimensions 11 m, 7 m, and 13 m. 2. **Formula for surface area of a rectangular prism:**

1. **State the problem:** We need to find the total surface area of a cube with side length 19 cm, which represents the amount of wrapping paper used. 2. **Formula:** The surface a

1. **Problem Statement:** Rotate the triangle with vertices at $A(2,2)$, $B(4,2)$, and $C(4,4)$ by 90° clockwise about the origin. 2. **Formula for 90° Clockwise Rotation:**

1. **Problem Statement:** Reflect the triangle with vertices at $A(0,-4)$, $B(2,-4)$, and $C(2,-6)$ over the vertical line $p$ given by $x = -2$. 2. **Reflection Formula:** For a p

1. The problem asks for the coordinates, but we need more context to determine which coordinates are required. 2. Coordinates usually refer to points in a plane or space, often giv

1. **Problem Statement:** Reflect the triangle with vertices at $ (2, -4), (4, -2), (4, -4) $ over the vertical line $ p $, which is the y-axis ($ x=0 $). 2. **Reflection Rule:** W

1. **Problem statement:** Reflect the quadrilateral with vertices at $(-7,1)$, $(-6,4)$, $(-3,3)$, and $(-3,0)$ across the vertical line $n$ which is the $y$-axis ($x=0$). 2. **Ref

1. **State the problem:** We have points $X(-2,-2)$ and $X'(-1,0)$, and points $Y(-6,1)$ and $Z(-4,2)$. Points $Y$ and $Z$ are translated by the same vector that moves $X$ to $X'$.

1. **State the problem:** We have two similar triangles DAR and KMR. We know side lengths DA = 16, DR = 11, MR = 14, and we want to find the unknown side length $y = KR$ in triangl

1. **State the problem:** We need to find the length of the minor arc on a circle of radius $r=3$ subtended by an angle of $0.687\pi$ radians. 2. **Formula for arc length:** The le

1. State the problem: Arrange the steps to draw a bearing of 055° from point X in the correct order. 2. Step 1: Draw a vertical line from point X to represent North.

1. **State the problem:** We have a square and a regular hexagon sharing a common side. The perimeter of the square is 24 inches. We need to find the perimeter of the hexagon. 2. *

1. **Problem Statement:** We are given a triangular race track on a Cartesian plane with vertices at $(-2,0)$, $(2,0)$, and $(0,4)$. Each grid square represents an area of 9245 m².

1. Problem 17: Find the total distance an ant travels from point (3,4) to (6,10), then from (6,10) to (10,18) in the Cartesian plane. 2. To find the distance between two points $(x

1. **State the problem:** We need to find the length of the hypotenuse of an isosceles right triangle where each leg measures 12 cm. 2. **Recall the formula:** In an isosceles righ

1. **Problem statement:** We have four collinear points A, B, C, and D arranged such that A - B - C and A - D - B. Given lengths are $AC = 84$ metres, $BC = 5$ metres, and $AD = 61

1. **Problem statement:** Given a circle with center at point $P$, two radii $A$ and $B$ form an angle of $286^\circ$ at $P$. We want to understand the properties of this angle in

1. **State the problem:** We have a diagram with points A, B, C, D, E, F on a gray plane and point G off the plane. We need to answer questions about the plane, coplanar points, no

1. **Problem statement:** Given points A, B, C, D on a circle, with lines AEC and DEB straight, and triangle AED equilateral, prove that triangle ABC is congruent to triangle DCB.

1. The problem is to classify the given quadrilateral based on its properties. 2. The quadrilateral has markings indicating all four sides are congruent (equal in length).