📐 geometry

1. The problem is to find the radius $r$ of a circle given its area $A = 25$ cm² and the formula for the area of a circle $A = \pi r^2$. 2. The formula for the area of a circle is:

1. **State the problem:** We have a parallelogram PQRS with \(\angle Q = 128^\circ\). We need to find the measure of \(\angle S\). 2. **Recall properties of parallelograms:** Oppos

1. **Problem statement:** We are given a parallelogram $PQRS$ with side $RS=5$, side $SP=3$, and angle $Q=128^\circ$. We need to find the length of side $QP$. 2. **Recall propertie

1. **Stating the problem:** We are given a quadrilateral ABCD with diagonals AC and BD intersecting at point E. We need to find the measures of angles $\angle BCD$, $\angle ABD$, $

1. **Stating the problem:** We are given a rectangle ABCD with diagonals intersecting at point E. We know that $m\angle ADE = 16^\circ$ and $m\angle AEB = 16^\circ$. We need to fin

1. **State the problem:** We are given two rectangles ABCD and WXYZ. For ABCD, angles and some measures are given, and for WXYZ, side WZ is expressed as $7x - 6$. We need to find t

1. The problem states that the figure is dilated by a factor of 2 centered at the origin. This means each point of the figure will be moved away from the origin by twice its origin

1. The problem states that a figure is dilated by a factor of $\frac{3}{2}$ centered at the origin. We need to find the coordinates of the resulting image after dilation. 2. The fo

1. The problem is to understand the length of side BC, which is given as 11 cm. 2. Since BC is a side length, no formula is needed to verify its length unless part of a larger prob

1. **Problem statement:** We have a polygon ABCDE with given side lengths: AB = 7 cm (horizontal), BC = 8 cm (vertical), CD = 5 cm (horizontal), DE = 2 cm (vertical). We need to fi

1. **State the problem:** Find the area of a regular pentagon with an apothem of 5 units. 2. **Formula for the area of a regular polygon:**

1. **Problem statement:** We have triangle ACD with a smaller triangle ABE inside it. Line BE is parallel to line DC. Given lengths: AB = 12 cm, AC = 15 cm, BE = 8 cm. We need to f

1. The problem is to generate an image showing the three different altitudes of a triangle. 2. An altitude of a triangle is a perpendicular segment from a vertex to the line contai

1. The problem asks if point O is the orthocenter of triangle ABC. 2. The orthocenter of a triangle is the point where all three altitudes intersect.

1. **State the problem:** We have two adjacent triangles sharing a side of length 11. One triangle has sides 15 and 11 with an angle of 75° opposite the side of length 15. The othe

1. **State the problem:** We have two triangles with equal sides and given angles. We want to find the range of possible values for $x$ such that the side lengths and angles are co

1. The problem is to calculate the length of the right side of a right triangle. 2. We use the Pythagorean theorem which states that in a right triangle, the square of the hypotenu

1. The problem involves a right triangle with one angle of 45° and the base (askelmitta) length of 65 units. 2. Since one angle is 45° and the triangle is right-angled, the other n

1. **Problem statement:** We have a parallelogram with sides $a$ and $b$ and an angle $\alpha$ between them. Internal bisectors of the angle are drawn, and we need to find the area

1. **State the problem:** Given a circle with points L, X, W, and N on its circumference, and two intersecting lines crossing outside the circle at point V, where $m\angle WX = 62^

1. The problem is to find the length of the hypotenuse of a right triangle using Pythagoras' theorem or basic trigonometry. 2. Pythagoras' theorem states that in a right triangle,