📐 geometry

1. **State the problem:** We have a patchwork motif made up of squares and right-angled isosceles triangles. We need to find the fraction of the whole motif that is shaded and expr

1. **Problem statement:** Find the surface area of a cube with side length 5 cm. 2. **Formula:** The surface area $A$ of a cube with side length $s$ is given by:

1. **Stating the problem:** We have a polygon composed of 7 squares arranged in a T-shape. Each square has side length $a$. The total area $A$ of the polygon is given as 288 m². We

1. **Stating the problem:** We have a figure composed of three smaller semicircles each with diameter $2$ m arranged side by side, and a larger semicircle enclosing them with diame

1. **State the problem:** We have a square divided into four triangles P, Q, R, and S.

1. **State the problem:** We are given a square ABCD with two smaller shaded squares X and Y inside it. We need to find the fraction of the area of ABCD that is shaded.

1. The problem involves three parallel lines \(\overline{BC} \parallel \overline{DE} \parallel \overline{FG}\) and points on these lines forming segments. We need to complete each

1. **Stating the problem:** We have a triangle EFG with a segment CD inside it parallel to FG. Given lengths are $EC=32$, $ED=40$, and $FC=24$. We need to find the length of segmen

1. **State the problem:** Find the area of a composite shape consisting of a rectangle and a semicircle on top. 2. **Identify dimensions:** The rectangle is 3 units wide and 4 unit

1. The problem asks which sequence of transformations maps quadrilateral ABCD onto quadrilateral EFGH. 2. The vertices of ABCD are A(2,0), B(2,4), C(4,4), D(6,0).

1. The problem involves understanding the properties of a circle, including its radius and diameter. 2. The radius of a circle is the distance from the center to any point on the c

1. The problem states that triangles $\triangle KLM$ and $\triangle NOM$ are similar, written as $\triangle KLM \sim \triangle NOM$. 2. In similar triangles, corresponding sides ar

1. **State the problem:** Triangle DEF is formed by connecting the midpoints of the sides of triangle ABC. The sides of DEF are given as DE = 2, EF = 3, and DF = 4. We need to find

1. **State the problem:** We have two intersecting lines forming four angles: $(3x + 33)^\circ$, $(16y + 10)^\circ$, $(25y - 8)^\circ$, and $(4x - 2)^\circ$. Opposite angles are eq

1. **State the problem:** Determine if triangles $\triangle ADE$ and $\triangle BEC$ are similar by AA similarity and find the correct similarity statement. 2. **Recall AA similari

1. **Stating the problem:** We have a triangle inscribed in a circle with two known angles: one is 70° adjacent to side $n$, and another is 50°. We need to find the measure of angl

1. **State the problem:** We are given three rays originating from point N: NL, NK, and NM. The angles are:

1. **State the problem:** We are given two intersecting lines forming vertical angles. One angle measures 104° and the opposite angle measures $4(x+1)^\circ$. We need to find the v

1. **State the problem:** Find the missing side $x$ in right triangles given an angle and one side. 2. **Recall formulas:**

1. The problem states that a polygon with vertices at points $D(-10,-8)$, $G(-6,8)$, $F(8,8)$, and $E(5,-4)$ is dilated by a factor of $\frac{3}{4}$ centered at the origin. 2. The

1. **State the problem:** We have an equilateral triangle with side length 7 units. 2. **Understand the transformation:** The triangle is translated 3 units to the right.