📐 geometry

1. **State the problem:** We need to find a way to divide the given figure, which consists of three adjacent rectangles, to calculate its total area. 2. **Identify the rectangles a

1. **State the problem:** Prove that triangles $\triangle VYZ$ and $\triangle YWX$ are similar given that $\angle VYZ = \angle YWX$, $HL = HE = LE$, and $m\angle VYZ + m\angle ZZYX

1. The problem asks to identify which image shows the blue image and to describe the resulting transformation. 2. From the description, the blue image corresponds to option B, wher

1. The problem is to find the area of a circle given the radius. 2. The formula for the area of a circle is $$A = \pi r^2$$ where $r$ is the radius.

1. **State the problem:** Find the total surface area of two stacked cylinders. 2. **Given data:**

1. **State the problem:** We have a right triangle with two 45° angles, meaning it is an isosceles right triangle (45°-45°-90° triangle). One leg is given as $\sqrt{12}$, and we ne

1. The problem states that the triangle is equilateral, meaning all sides are equal in length. 2. The triangle has a right angle, which is unusual for an equilateral triangle becau

1. **State the problem:** We have a circle with radius $R=6400$ km and a central angle $X=22^\circ$. We want to find the length of the arc subtended by this angle. 2. **Formula use

1. **State the problem:** We are given a unit circle with equation $$x^2 + y^2 = 1$$ and a point on the circle with coordinates $\left(\frac{1}{3}, y\right)$. We need to find the v

1. **State the problem:** We need to find the volume of the red book (bottom prism) and then find the total volume of both prisms stacked together. 2. **Recall the formula for volu

1. **State the problem:** We need to find the value of $x$ in a right triangle where the sides given are 23 and 34, and $x$ is the unknown side. 2. **Identify the formula:** In a r

1. The problem is to find the value of $x$ in a triangle where the sides are given as 23, 34, and $x$. 2. We assume this is a right triangle and use the Pythagorean theorem: $$a^2

1. **State the problem:** We need to find possible dimensions for rectilinear shapes with given perimeters. 2. **Recall the perimeter formula:** For rectilinear shapes, the perimet

1. **State the problem:** We need to find the images of the vertices of triangle $\triangle PQR$ under a dilation centered at $(0,0)$ with scale factor 2. 2. **Recall the dilation

1. **State the problem:** We need to find the length of side $g$ in triangle $GEF$ where angles and some sides are given. 2. **Given:**

1. **State the problem:** We have a dilation of a black polygon to a blue polygon with center of dilation at point $P$. We need to determine if the dilation is an enlargement or re

1. Problemet är att hitta arean som är 1700 cm². 2. Om vi antar att vi har en rektangel eller annan figur, måste vi veta dess dimensioner eller formel för att bekräfta detta.

1. Problemet är att beräkna arean av triangeln ABC där vi vet att det är en rätvinklig triangel med en katet (sida intill den räta vinkeln) på 40 cm och hypotenusan på 60 cm. 2. Fo

1. Problem (i): Prove that a point O equidistant from points A and B lies on the perpendicular bisector of segment AB. 2. Recall the definition: The perpendicular bisector of a seg

1. **State the problem:** We have a large cone with height $42$ mm and radius $6$ mm. It is split horizontally into a smaller similar cone at the top with height $14$ mm and radius

1. **State the problem:** We need to find the volume of the frustum of a rectangular-based pyramid. The frustum is formed by cutting a larger pyramid horizontally, leaving a smalle