📐 geometry

1. Problem (a): Complete the pseudo code to calculate the area of a sector with radius $r$ and angle $\theta$. The formula for the area of a sector is $$\text{Area} = \frac{\theta}

1. **State the problem:** A cone with base radius $r=6$ cm and height $H=36$ cm is cut parallel to its base, forming a smaller cone on top and a frustum below. The frustum volume i

1. **Problem statement:** Given a circle with center $O$, tangents $PA$ and $PB$ from point $P$ touch the circle at points $A$ and $B$ respectively. Given angles are $\angle APB =

1. **Problem statement:** Given a circle with center O, tangents PA and PB from point P touch the circle at A and B respectively. Given angles: \(\angle APB = 48^\circ\) and \(\ang

1. **State the problem:** We are given a parallelepiped prism with edges 4 cm, 12 cm, 12 cm, and one edge labeled as $3x + 20$ cm. The total surface area is 504 cm$^2$. We need to

1. **State the problem:** We are given a parallelepiped prism with a surface area of 504 cm². The dimensions include a height of 4 cm, a side length of 12 cm, and a slant edge leng

1. مسئله: یک پنج ضلعی منتظم رسم کنید و محورهای تقارن آن را مشخص کنید. 2. تعریف: پنج ضلعی منتظم شکلی است که پنج ضلع برابر و پنج زاویه برابر دارد.

1. **Stating the problem:** We need to calculate the ratio $\frac{a}{b}$ where $a$ is the height of the semicircle (which is its radius) and $b$ is the radius of the smaller circle

1. **State the problem:** We have a figure made up of a rectangle, a square, and a right-angled triangle. The area of the square is \(\frac{2}{11}\) of the total area of the figure

1. Let's first understand the problem: You want to know if it is correct to write $AD=BE$ (by C.P.C.T) directly without stating that both triangles are congruent first. 2. C.P.C.T

1. The problem is about understanding if the equality $AD = BA$ is the same as $BA = AD$ in the context of triangle congruency. 2. In mathematics, equality is symmetric, meaning if

1. Problem (i): Given squares with areas 7 cm², 17 cm², and 10 cm², determine if they surround a right angled triangle. 2. Step 1: Recall the Pythagorean theorem states for a right

1. Find the sizes of the labelled angles. a. Given angles: 87°, 112°, 95°.

1. **Problem statement:** Given a kite formed by an equilateral triangle BCD and an isosceles triangle ABD with \(\angle ABC = 90^\circ\), find \(\angle BAD\) and other labelled an

1. The problem is to find the distance between points $A(4,-3)$ and $B(3,-4)$.\n\n2. Use the distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$: $$d = \sqrt{(x_2 - x_1

1. **Énoncé du problème** : Trouver une équation du plan (P) passant par les points A(3,1,1), B(2,0,3), C(1,2,2). 2. **Calcul du vecteur normal au plan (P)** :

1. **State the problem:** We have a rectangle with width 17 cm and height 8 cm. On the left side, there is a quarter circle arc with radius 8 cm (the height), and on the right side

1. **Problem statement:** We have an isosceles triangle LMN with LM = LN. Lines AMB and CLN are parallel.

1. **State the problem:** We have two similar rectangles. The smaller rectangle has dimensions $4 \text{ cm}$ by $7 \text{ cm}$. The larger rectangle has one side $4.8 \text{ cm}$

1. نبدأ بتحديد المعطيات المعروفة من الشكل: \( \angle W = 80^\circ \), \( \angle P = 48^\circ \), و\( \angle R = 47^\circ \). 2. المعطى أن \( OW \) خط أفقي، و\( \angle W = 80^\circ

1. **Statement of the problem:** Given two intersecting lines with a horizontal line passing through points A, B, and C (B below segment AC), and a diagonal line crossing near C fo