📐 geometry

1. **State the problem:** We need to find the translation rule that maps segment JK to segment J'K'. 2. **Given points:**

1. The problem asks for the translation rule that maps triangle \(\triangle CDE\) to \(\triangle C'D'E'\).\n\n2. A translation moves every point of a figure the same distance in th

1. The problem asks for the translation rule that maps triangle \(\triangle STU\) to \(\triangle S'T'U'\).\n2. The given points are:\n- \(U(-9,-1)\) to \(U'(4,8)\)\n- \(T(-5,-5)\)

1. The problem asks for the translation rule that maps quadrilateral DEFG to quadrilateral D'E'F'G'. 2. A translation moves every point of a figure the same distance in the same di

1. The problem asks for the translation rule that maps quadrilateral DEFG to quadrilateral D'E'F'G'. 2. A translation moves every point of a shape by the same amount horizontally a

1. **State the problem:** We need to find the volume of a cylindrical can with radius $r = 3.6$ cm and height $h = 10$ cm. 2. **Formula for volume of a cylinder:** The volume $V$ i

1. **State the problem:** We want to find the perimeter of a triangle, which is the total length around the triangle. 2. **Formula:** The perimeter $P$ of a triangle is the sum of

1. **State the problem:** A sandpile forms a mound where the slant side RT is 20 meters and makes a 40° angle with the ground at point R. We need to find the volume of the sandpile

1. **State the problem:** We need to find the length of the diagonal path across a square garden that measures 100 feet on each side. 2. **Formula used:** The diagonal $d$ of a squ

1. **State the problem:** Find the volume of a cone with radius $r=4$ m and height $h=15$ m, expressing the answer in terms of $\pi$. 2. **Formula for the volume of a cone:**

1. **Problem 11:** A cone with diameter 10 m has surface area 290.6 m². Find its slant height. 2. **Formula for surface area of a cone:**

1. **State the problem:** Find the area of a regular pentagon with an apothem (distance from center to a side) of 19 m. 2. **Formula:** The area $A$ of a regular polygon is given b

1. **Problem:** Sketch a cylinder with radius 3 and height 10, and shade one of its bases. 2. **Formula and explanation:** A cylinder is a 3D shape with two parallel circular bases

1. **Problem:** In a right triangle, one shorter side is 6 units and the hypotenuse is 10 units. Find the length of the other shorter side. 2. **Formula:** Use the Pythagorean theo

1. **State the problem:** Find the area of a circle given its diameter is 15 cm.

1. **State the problem:** We have a triangle with angles labeled as 63°, (8x - 17)°, and (3x + 2)°, and we are given that $x = 12$. We need to find the measures of all angles. 2. *

1. **Problem Statement:** Find the area of a square given its diagonal length is 11 m. 2. **Formula and Rules:** For a square with side length $s$ and diagonal length $d$, the rela

1. **State the problem:** We need to find the area of a circle with a diameter of 20 inches. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. **State the problem:** We need to find the area of a circle with a diameter of 17 inches. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. **State the problem:** Find the missing length in the first triangle proportionality problem where the given lengths are 10, 4, 6, and the missing length is ?. The proportion is

1. **State the problem:** We need to find the area of a circle with radius $r = 3$ cm. 2. **Formula:** The area $A$ of a circle is given by the formula: