📐 geometry

1. **Problem 1.a:** In parallelogram ABCD, given that angle \(\angle DAB = 60^\circ\), find angle \(\angle C\). 2. **Formula and properties:** In any parallelogram, opposite angles

1. **Problem Statement:** In parallelogram ABCD, we are given that angle \(\angle DAB = 60^\circ\). We need to find the measure of angle \(\angle C\).

1. **State the problem:** We need to find the total area of the two shaded faces of a cuboid with dimensions 7 cm (height), 9 cm (width), and 12 cm (length). The shaded faces are t

1. **State the problem:** Calculate the areas of faces A, B, and C on a cuboid with given dimensions. 2. **Identify the dimensions:**

1. **Problem statement:** Given a rectangular prism with side lengths $a=11.6$ cm, $b=9.7$ cm, and $c=14.3$ cm, and $M$ as the midpoint of segment $SR$, calculate the size of angle

1. The problem asks to find the value of angle $B$ in the context of a square ABCD with side length 22 cm and an inscribed circle. 2. Since ABCD is a square, all its interior angle

1. The problem asks to identify the type of quadrilateral ABCD. 2. To determine the type of quadrilateral, we need information such as side lengths, angles, or coordinates of point

1. **Problem Statement:** Determine the type of triangle \(\triangle ABC\) formed by points \(A(-4,2)\), \(B(-4,-6)\), and \(C(2,-6)\). Also, check if it is a right triangle. 2. **

1. **Problem Statement:** Calculate the area of a compound figure made up of five rectangles with given dimensions. 2. **Approach:** The total area of the compound figure is the su

1. The problem asks to find the translation that maps point $P(-3, 1)$ to point $P'(1, 5)$. 2. A translation moves a point horizontally and vertically by certain units. The formula

1. **State the problem:** We have a point $Q(6,4)$ that is translated to $Q'(3,2)$. We need to find the translation vector.

1. **State the problem:** Calculate the volume of a triangular prism with a triangular base of base length 12 cm and height 8 cm, and prism length 20 cm. 2. **Formula:** The volume

1. **Problem Statement:** We have a right triangle with vertices at the origin $(0,0)$, a point on the unit circle, and a point on the x-axis inside the unit circle. We need to fin

1. **State the problem:** We need to find the perimeter $p$ of an irregular L-shaped polygon with four right angles and sides measuring 2.5 ft., 1.25 ft., 1.25 ft., and 2.5 ft. 2.

1. **Problem statement:** Find the perimeter of the shape combining a square of side 14 cm and a semicircle of radius 7 cm attached to one side. 2. **Formula:** The perimeter $P$ o

1. **State the problem:** We need to find the volume of a rectangular prism made up of unit cubes, where each cube has side length 1 cm. 2. **Given dimensions:** The prism is 3 cub

1. **State the problem:** We need to find the length of the missing side $a$ in a right triangle where the hypotenuse is 20 and one leg is 16. 2. **Formula used:** In a right trian

1. Énonçons le problème : Nous avons un axe des abscisses avec plusieurs points et une parabole avec un sommet S à une hauteur $h$. Le point $I$ est situé en $(44,0)$. 2. On sait q

1. **State the problem:** We need to find the coordinates of the point that is $\frac{3}{10}$ of the way from point $A(0,0)$ to point $B(10,9)$.\n\n2. **Formula used:** To find a p

1. **State the problem:** Find the coordinates of the point that lies $\frac{3}{10}$ of the way from point $A(-5, -8)$ to point $B(12, 6)$.\n\n2. **Formula used:** The coordinates

1. **Stating the problem:** Given that \(\angle 3 = 74^\circ\), find the measures of other related angles formed by two parallel lines \(l\) and \(m\) cut by two transversals. 2. *