📐 geometry

1. **State the problem:** We have trapezoid JKMN with area 136 square km. The base KM is 20 km, and the height (distance from KM to JN) is 8 km. We need to find the area of triangl

1. **State the problem:** The angles of a triangle are in the ratio 1:3:5. We need to find the measure of the largest angle. 2. **Recall the rule:** The sum of the angles in any tr

1. **State the problem:** We have two concentric circles. The inner circle has radius $19$ yd, and the ring-shaped path around it has a width of $5$ yd. We want to find the area of

1. **Problem Statement:** Given triangle $\triangle JKL$ with incenter $P$, and the lengths $PO=31$, $KM=34$, and $PL=48$, find the lengths of segments $PM$, $KN$, $OL$, and $KP$.

1. **State the problem:** Given that $\angle FCE \cong \angle DEC$ and $\angle FCD \cong \angle DEF$, prove that quadrilateral $CDEF$ is a parallelogram. 2. **Recall the definition

1. **State the problem:** Find the volume of a right circular cone with height $h=7$ yards and slant height $l=9$ yards. 2. **Recall the formula for the volume of a cone:**

1. **State the problem:** Find the volume of a cone with radius $r=5$ cm and height $h=8$ cm. 2. **Formula for the volume of a cone:**

1. **State the problem:** We are given a cylinder with a radius $r = 5$ mm and a total surface area $S = 440$ square millimeters. We need to find the height $h$ of the cylinder. 2.

1. **State the problem:** We need to find the total surface area of a figure made of two stacked cylinders: a smaller top cylinder with height 3 cm and radius 5 cm, and a larger bo

1. **State the problem:** Find the circumference of a circle with radius $r=3.3$ m using $\pi=3.14$. 2. **Formula:** The circumference $C$ of a circle is given by

1. **State the problem:** A bicycle tire has a diameter of 22 inches. We want to find how many feet the bicycle travels when the wheel makes 20 revolutions, rounding to the nearest

1. **State the problem:** A bicycle tire has a diameter of 22 inches. We want to find how many feet the bicycle travels when the wheel makes 20 revolutions. Round to the nearest hu

1. The problem states that the figure KL is rotated 180° counterclockwise about the origin to produce K'L'. 2. The rule for a 180° counterclockwise rotation about the origin in the

1. The problem states that line segment LM is rotated 180° counterclockwise about the origin to produce L'M'. 2. The rule for a 180° counterclockwise rotation about the origin is:

1. **State the problem:** We have a scale drawing where 2 cm represents 3 m. The bedroom is a rectangle with dimensions 2 cm by 4 cm in the drawing. We need to find the actual area

1. **State the problem:** We have a scale drawing where 1 cm represents 3 m in real life. The patio is rectangular with dimensions 4 cm by 3 cm in the drawing. We need to find the

1. **Problem statement:** A cylinder is inscribed in a sphere of radius 8 inches. We need to find the maximum volume of this cylinder. 2. **Known values and variables:**

1. Énoncé du problème : Calculer la longueur BC dans un triangle ABC où AB = 6, AC = 3 et l'angle BAC = $\frac{\pi}{6}$.\n\n2. Formule utilisée : Pour calculer un côté dans un tria

1. **State the problem:** We need to find the center of dilation that maps triangle ABC with vertices A(-4,-5), B(3,-5), C(-1,-1) to triangle A'B'C' with vertices A'(-4,1), B'(8,1)

1. **State the problem:** We have a right triangle with a base of $\frac{5}{4}$ cm, one leg of $\frac{3}{4}$ cm, and a hypotenuse of 1 cm. We need to find the area of the triangle.

1. The problem asks to find the coordinates of point A. 2. To find coordinates of a point, we need information such as its position relative to axes or other points.