📐 geometry

1. **Problem Statement:** We have a parallelogram ABCD with sides given as: - AB = $3x - 5$ cm

1. **State the problem:** Calculate the area of the composite shape that looks like a right-pointing arrow with given dimensions: height 6 ft on the left, width 7 ft at the bottom,

1. **Problem Statement:** We are given triangle L M N with vertices approximately at $L(2,2)$, $M(5,6)$, and $N(6,3)$, and its image triangle L' M' N' with vertices approximately a

1. **State the problem:** Determine if triangles \(\triangle JKL\) and \(\triangle MNP\) are similar, and if so, identify the correct similarity criterion. 2. **Given data:**

1. **Problem statement:** We have triangle $\triangle LMN$ with vertices $L(2,2)$, $M(6,6)$, $N(6,2)$ and its image $\triangle L'M'N'$ with vertices $L'(11,2)$, $M'(7,6)$, $N'(7,2)

1. **State the problem:** We have a rectangle with width $14x$ and height $y$. There are two shaded strips: one at the top with height $x - 8$ and one on the right side with width

1. **Problem:** Find the unknown angle at vertex R in parallelogram RQST where angle at S is 135°. 2. **Formula and rules:** In a parallelogram, opposite angles are equal, and adja

1. **State the problem:** We are given the circumference of a circle as 165 mm and need to find the area of the circle, rounded to 1 decimal place. 2. **Recall the formulas:**

1. **State the problem:** We have a small rectangle with a height of 12 mm and an unknown width. Fourteen copies of this small rectangle are arranged in a larger rectangle composed

1. **State the problem:** We have four identical rectangles each measuring 8 cm by 3 cm arranged around a smaller purple square. We need to find the area of this purple square. 2.

1. **Problem statement:** We have two triangles PQR and RST sharing vertex R on the same baseline. Given angles \(\angle Q = 76^\circ\) and \(\angle S = 102^\circ\), sides QP = QR

1. **State the problem:** We need to find the measure of angle $\angle N$ in an isosceles triangle $\triangle NPM$ where sides $NM$ and $MP$ are equal. 2. **Identify given informat

1. **Problem statement:** Calculate the length $d$ of the cable, which is the hypotenuse $AD$ of the right triangle $ABCD$ with sides $AB=45$ m, $BC=9$ m, and $DC=28$ m. 2. **Under

1. **Énoncé du problème :** Soit un triangle rectangle en B avec les points A, B, C.

1. **Problem statement:** Calculate the perimeter of each figure given the side lengths. 2. **Formula for perimeter:** The perimeter $P$ of a polygon is the sum of the lengths of a

1. **Problem statement:** Find the coordinates of point B where the circle centered at O intersects the x-axis, and find the equation of the line on which the diameter BD lies. 2.

1. **Problem Statement:** In an acute angled triangle, AD is the median and AE is the altitude. Prove that $$C^2 = AD^2 + BC \times DE + \frac{1}{4} BC^2$$. 2. **Understanding the

1. **State the problem:** Construct a parallelogram ABCD where side AB = 6 cm, side AD = 3 cm, and the angle at vertex A is 60 degrees. 2. **Recall properties and formulas:**

1. **State the problem:** We need to find the value of $x$ given a right triangle with a vertical leg labeled $3x + 6$ and a horizontal leg labeled $30$. 2. **Understand the proble

1. **State the problem:** We need to find the value of $x$ given a right triangle where the vertical side is labeled $3x + 6$ and the horizontal side is labeled $30$. 2. **Understa

1. **State the problem:** Given a diamond-shaped quadrilateral PQRS with diagonals PR and QS intersecting at T, where PR is the perpendicular bisector of QS. Given lengths: PS = 10