📐 geometry

1. **State the problem:** We need to find the perimeter and area of a rectangle with vertices A(-6, 2), B(7, 2), C(-6, -8), and D(7, -8). 2. **Recall formulas:**

1. **State the problem:** We have a rectangle ABCD with vertices A(-6,9), B(4,9), C(-6,-3), and D(4,-3). We need to find: a) The perimeter of the rectangle.

1. **Problem 2:** In the isosceles triangle $ABC$ with $AB = AC$, and $KL = LM$, given $LC = 12$, find $KB$. 2. Since $AB = AC$, triangle $ABC$ is isosceles with $B$ and $C$ at the

1. **Problem statement:** Triangles $\triangle ABC$ and $\triangle XYZ$ are similar right-angled isosceles triangles. Squares $KLM B$ and $PQRS$ inside them have equal areas. Given

1. **State the problem:** Calculate the volume of an oblique rectangular prism whose base is a parallelogram with base length 9 units and height 8 units, and the prism extends back

1. **State the problem:** We need to find the horizontal distance between points A and B on the coordinate plane. 2. **Identify the coordinates:** Point A is at $(0,4)$ and point B

1. The problem asks to find the equation resulting from applying the secant and tangent segment theorem to the given figure. 2. The secant and tangent segment theorem states that i

1. **State the problem:** We are given a circle with points A, B, D on a vertical line and a radius labeled $a$. Segments $AD=12$ and $AB=10$ are given. We want to find the equatio

1. **State the problem:** We need to find the area of the shaded segment in a circle with radius 12 cm and central angle 47°. 2. **Recall the formula:** The area of the segment is

1. **Problem statement:** Find the area of the shaded triangle inside a circle with radius 12 cm and central angle 47°. 2. **Formula for the area of a triangle with two sides and i

1. The problem involves two separate geometric setups with unknown $x$ values to solve for. 2. First problem: A triangle with a circle inside it, where one side is 14, a segment ad

1. The problem is to create a geometry paper for 10th grade English medium SSC, similar to SSC format. 2. Since this is a request for a paper format, not a specific math problem, w

1. **Problem statement:** We have a circle with points P, Q, R on the circumference and secants PS and RT intersecting outside the circle. Given segment lengths: $PT=2.4$, $PQ=7$,

1. The problem is to find a certain value or relationship using 2 triangles. 2. When using two triangles, common methods include comparing corresponding sides or angles, using simi

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

1. **State the problem:** We need to find the area of a circle with radius 18 ft in terms of $\pi$. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. Problem 14 to 30 includes multiple distinct questions, but per instructions, we solve only the first one, which is 25.a: Find the coordinates of M and draw the rectangle. 2. Giv

1. The problem is to find the length of the third side of a right triangle where the two legs are given as $7$ and $\sqrt{51}$.\n2. We use the Pythagorean theorem for right triangl

1. **State the problem:** We have a right triangle with two legs each of length 8, and we need to find the length of the third side (the hypotenuse). 2. **Formula used:** The Pytha

1. **Problem Statement:** Find the length of the zip line AD in a rectangular prism where the zip line runs diagonally from corner A to opposite corner D, making a 60° angle with p

1. **Problem Statement:** Determine the shortest path from Start to Finish on the obstacle course given three possible routes: - A. Start to A to D to Finish