📐 geometry

1. **State the problem:** We need to find the area of a composite figure made up of a parallelogram, a trapezoid, and a triangle with given dimensions.

1. **State the problem:** We need to find the combined area of the parallelogram and the triangle in the composite figure. 2. **Recall formulas:**

1. **State the problem:** We need to find the image of a triangle after reflecting it across the y-axis and then translating it by the vector $v=(-1,0)$. The original triangle has

1. **State the problem:** Given a circle with points T, S, R, Q on its circumference and angles $m\angle STQ = 246^\circ$ and $m\angle TSR = 123^\circ$, find: (a) $m\angle STQ$ (al

1. **Problem statement:** Given a circle with a triangle inscribed such that one angle is $46.8^\circ$ and the angle $x$ is on the opposite side of the diameter line, find the valu

1. **Stating the problem:** We are given two intersecting lines forming angles, with one angle labeled $x$ and the corresponding angle on the opposite side labeled $72^\circ$. We n

1. **State the problem:** We have a right triangle where the longer leg is 7 cm longer than the shorter leg, and the hypotenuse is 9 cm longer than the shorter leg. We need to find

1. **State the problem:** We have a right triangle with hypotenuse 13, one leg 7, and the other leg $x$. We need to find $x$ rounded to the nearest hundredth. 2. **Formula used:**

1. **State the problem:** We are given three vectors \(\overrightarrow{AB}\), \(\overrightarrow{CD}\), and \(\overrightarrow{CE}\) originating from point \(C\) with angles \(82^\ci

1. **State the problem:** Reflect the point $(2,0)$ across the line $y=x$. 2. **Formula and rule:** When reflecting a point $(a,b)$ across the line $y=x$, the coordinates swap plac

1. **State the problem:** We are given a circle with a radius of 4 cm and an arc measuring 70°.

1. **Problem statement:** We need to describe a sequence of rigid motions (translations, rotations, reflections) that maps figure ABCDEFG onto figure JKLMNPQ, given that they are c

1. **Stating the problem:** We have a polygon with points A, B, C, D, E, F, G, H. Given that $AC=26$, $D$ is the midpoint of $AC$, and $AD=BF$. We need to find the perimeter of the

1. **Problem statement:** Given a circle with center C and points A, B, D on the circumference, where $m\angle C = 35^\circ$, find: a) $m\angle LA$

1. **State the problem:** Find the circumference of a circle with diameter 88 mm to 1 decimal place. 2. **Formula:** The circumference $C$ of a circle is given by

1. **State the problem:** We are given a quadrilateral with angles 113°, 98°, 42°, and an unknown angle $x$. We need to find the value of $x$. 2. **Formula used:** The sum of the i

1. **State the problem:** Megan has two boxes with given dimensions. We need to find the volume of each box and determine which box has the greater volume to decide which one she s

1. **Problem statement:** Given a triangle with an exterior angle of 108° and one interior angle of 40°, find:

1. **State the problem:** A rectangle is dilated by a scale factor of $\frac{1}{2}$ to produce a new rectangle. We need to find the relationship between the perimeter of the origin

1. **State the problem:** We need to find the size of the exterior angle $x$ in a quadrilateral where the interior angles given are $90^\circ$, $80^\circ$, $65^\circ$, and one unkn

1. **State the problem:** We need to find the size of the exterior angle $x$ adjacent to the interior angle of $65^\circ$ in a quadrilateral. 2. **Recall the rule for exterior angl