📐 geometry

1. **Problem 13:** A round table cover has six equal designs. The radius of the cover is 28 cm. Find the cost of making the designs at the rate of 0.35 per cm². Use \( \sqrt{3} = 1

1. **Problem Statement:** We are given a quadrilateral STUV with the following properties: - $ST \cong UV$

1. The problem asks to find the translation rule that maps triangle $\triangle CDE$ to triangle $\triangle C'D'E'$.\n\n2. A translation moves every point of a figure the same dista

1. **State the problem:** We have triangle △VWX with vertices V(-10, 2), W(-7, 8), and X(-3, 2), and its translation △V'W'X' with vertices V'(4, -8), W'(7, -2), and X'(11, -8). 2.

1. **Problem statement:** Given a triangle with sides 38, 33, and an angle of 35° at vertex A adjacent to side 38, find the angle A and the length of side $x$ opposite the 35° angl

1. **Red: Reflect square STUV in the x-axis** The reflection rule in the x-axis is $(x,y) \to (x,-y)$.

1. **State the problem:** Locate each group of points on a Cartesian plane and join the points in each group separately.

1. The problem asks to write the coordinates of each point labeled A through I on a Cartesian coordinate plane. 2. The Cartesian plane has an x-axis (horizontal) and y-axis (vertic

1. **Problem statement:** Find the vertices of the triangle invariant under two transformations:

1. Problem 14: Given a figure with BC = 4, AB = 6, AD = 3 units, and \(\angle AEC = 90^\circ\), find the length of EC. 2. Since \(\angle AEC = 90^\circ\), triangle AEC is a right t

1. The problem involves performing dilations on points or shapes with given centers and scale factors $k$. 2. The dilation formula for a point $P(x,y)$ with center $C(x_c,y_c)$ and

1. **Stating the problem:** We have a triangle with a perpendicular dropped from the top vertex to the base, splitting the base into two segments of lengths 50 and 46 units. The si

1. مسئله: تعداد مکعب‌های موجود در تصویر را پیدا کنیم. 2. برای حل این مسئله، باید مکعب‌ها را به صورت جداگانه بشماریم و توجه کنیم که مکعب‌های بزرگ‌تر ممکن است از ترکیب چند مکعب کوچک‌

1. مسئله: تعداد مکعب‌های موجود در تصویر را بیابیم. 2. برای حل این مسئله، باید تعداد مکعب‌های کوچک، متوسط و بزرگ را جداگانه بشماریم و سپس جمع کنیم.

1. مسئله: تعداد مکعب‌ها را پیدا کنید. 2. برای محاسبه تعداد مکعب‌ها، باید بدانیم مکعب‌ها چگونه چیده شده‌اند یا ابعاد ساختار مکعبی چیست.

1. Statement of the problem: Find the area and centroid of the quadrilateral with vertices $D(5,4)$, $E(8,2)$, $F(7,-2)$, and $G(4,-4)$. 2. Formulas and rules used: Use the shoelac

1. The problem asks for the coordinates of point C on the given polygon. 2. From the graph description, the coordinates of the vertices are given explicitly.

1. **State the problem:** We have two shapes made from identical semicircles. The first shape has three semicircles with a total perimeter of 36 cm. We need to find the perimeter o

1. **State the problem:** We have a shape made of three identical semicircles with a total perimeter of 36 cm. We need to find the perimeter of a new shape made from the same semic

1. **State the problem:** We need to find the bearing of point Y from point W given the angles between rays from W. 2. **Understand bearings:** Bearings are measured clockwise from

1. We are asked to find the arc length of a partial circle with radius $7$. 2. The formula for the arc length $L$ of a circle segment is: