📐 geometry

1. **State the problem:** Annabel wants to know how much wood flooring she needs for her bedroom and closet. We need to find the total area of both rooms.

1. **State the problem:** We have two right triangles sharing a vertex, with the larger triangle having hypotenuse $w$ and base $x$, and the smaller triangle inside it having legs

1. **Problem Statement:** Determine the coordinates $(x_i, y_i)$ for $i=1$ to $5$ of five points equally spaced by angle on a quarter circle centered at the origin with radius 1, l

1. **State the problem:** We have a triangle with sides labeled 15, 12, and 10, and two horizontal segments inside it labeled $y$ and 4 on the upper segment, and $x$ on the lower s

1. **State the problem:** We have a large triangle with a base of 13 and two segments inside parallel to the base, creating smaller triangles with sides labeled 4, 6, 2, 6, 9, and

1. **State the problem:** We are given a circle with points O, M, P, N on the circumference and Q as the center. Angles at O and P are 62° and 94° respectively. We need to solve fo

1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°, and the hypotenuse is given as $7\sqrt{3}$ meters. We need to find the length $j$ of the side oppo

1. **State the problem:** We need to find the length $x = VU$ in the right triangle $\triangle VUT$ where $\angle U = 90^\circ$, $UT = 64$, and $\angle UTV = 70^\circ$. 2. **Identi

1. **State the problem:** We need to find the length of side $x = MN$ in a right triangle $MNO$ where the right angle is at $N$, side $NO = 7$, and angle $O = 52^\circ$. 2. **Ident

1. **State the problem:** We start with point $P(-6,1)$ and apply a series of transformations in the order given.

1. **State the problem:** Given two sides of a triangle, find which of the given options can be the length of the third side. 2. **Formula and rule:** For any triangle with sides $

1. **State the problem:** Given two side lengths of a triangle, determine which of the given options can be the third side length. 2. **Recall the triangle inequality theorem:** Fo

1. The problem asks to measure and classify triangles by their angles and sides. 2. To classify by angles:

1. **State the problem:** We have two similar rectangles D and E. Rectangle D has width 8 mm and height $x$ mm.

1. The problem involves finding the perimeter of compound shapes made up of smaller rectangles arranged in various "L" or "T" patterns. 2. The perimeter of a compound shape is the

1. **State the problem:** We need to find the exact volume of a cylinder with diameter 3 inches and height 5 inches. 2. **Formula for the volume of a cylinder:**

1. **Problem:** Find the value of $\angle BCA$ in the triangle where the side opposite $B$ is labeled $2x$. 2. **Formula and rules:** In any triangle, the sum of interior angles is

1. **State the problem:** We are given three angles with expressions in terms of $x$ and $y$: - $m\angle 5 = 2x + 3y$

1. **State the problem:** Find the area of the composite figure composed of a large rectangle with a smaller rectangle and a right triangle cut out from the bottom left. 2. **Ident

1. **State the problem:** We have two similar triangles \(\triangle ABC\) and \(\triangle XYZ\). Given sides are \(AB=5\), \(AC=7\), and unknown side \(BC=?\) in \(\triangle ABC\),

1. **Stating the problem:** We have a right-angled triangle with one angle marked as 90° and two other angles labelled as $f$ and $o$. We want to understand the relationship betwee