📐 geometry

1. **Problem statement:** A plot of land has an area of 876 m² and is divided into three rectangular fields of equal width. The total fencing used is 177 m, which includes the peri

1. **Problem:** Find the perimeter of triangle \(\triangle MNP\) where sides are given as \(5x - 34\), \(25\), and \(22\), and angle at \(P\) is \(x + 4\). We need to find the peri

1. **Identify all pairs of parallel segments.** Given the parallelogram and segments:

1. **Problem statement:** Calculate the side length of the equilateral triangle inscribed in an isosceles right triangle with base $c=12.0$ cm as shown in Abb. 3.150 a).

1. **State the problem:** We have three identical rectangles arranged in an L shape on the coordinate plane. The bottom-left corner of the bottom-left rectangle is at point $(1,4)$

1. **Problem statement:** We have a quadrilateral subdivided into two triangles by a segment DE parallel to AB. Given lengths are $AB=8$, $DE=5$, and $BC=10$. We need to find the l

1. The problem states that segments AB and DE are parallel, and we have two triangles ABC and DCE with given side lengths. We need to find the length $x$ of segment CD. 2. Since AB

1. The problem asks for a degree of rotational symmetry of a regular pentagon. 2. A regular pentagon has 5 equal sides and 5 equal angles.

1. **State the problem:** We need to find the radius $r$ of a circle given its circumference $C = 69.08$ feet. 2. **Formula used:** The circumference of a circle is related to its

1. **State the problem:** We need to find the circumference $C$ of a circle with diameter $d = 15$ feet. 2. **Formula:** The circumference of a circle is given by the formula:

1. The problem asks us to determine if John and Miles beat or missed their goal of canoeing at least 14 miles based on the graph. 2. The path starts at point $(-7,-2)$ and ends at

1. **State the problem:** We need to find the scale factor used to transform rectangle X into rectangle Y and express it as a percentage to one decimal place. 2. **Identify given d

1. The problem asks to identify two words that describe each of the seven triangles based on their angles and side lengths. 2. Important definitions:

1. The problem asks to identify two words that describe each triangle based on its properties. 2. Important definitions:

1. **State the problem:** Classify each triangle based on its angles as acute, obtuse, or right. 2. **Recall definitions:**

1. The problem asks why the height is not explicitly given for the second hay bale, which is a cylinder. 2. For a cylinder, the volume formula is $$V = Bh = \pi r^2 h$$ where $r$ i

1. **State the problem:** Calculate the volume of a cylindrical hay bale with diameter 5 ft and height 4 ft using the formula for the volume of a cylinder. 2. **Formula:** The volu

1. The problem is to classify triangles by their angles and sides. 2. For angles:

1. The first solid figure is a prism because it has two parallel and congruent triangular bases connected by rectangular faces. 2. The second solid figure is a pyramid because it h

1. **State the problem:** We have a right triangle ABC with a right angle at C. Angle B is 30°, angle A is 60°, and the side opposite angle B (which is side AC) is labeled $2\sqrt{

1. **State the problem:** We are given two angles formed by intersecting lines: one angle is $3x$ degrees and the other is $30$ degrees. We want to find the value of $x$. 2. **Unde