📐 geometry

1. Let's understand the problem: We need to find the perimeter and area of regular figures, volume and surface area of solids, and area of irregular figures using mathematical meth

1. **State the problem:** We need to find the total area of a composite figure made of two parts: a rectangle on top and a trapezoid below. 2. **Identify the shapes and their dimen

1. **Problem statement:** Find the missing angles \(\angle 1\) and \(\angle 2\) in each figure and provide a reason for the answer. ### Part a)

1. Problem 3: Find the volume of the bottle crate, a rectangular prism with dimensions 90 cm (length), 60 cm (width), and 80 cm (height). 2. Volume of a rectangular prism is given

1. **Shape a**: Two quarter circles joined at a right angle, height 28 cm. - Each quarter circle radius $r=28$ cm.

1. ප්‍රශ්නය: වෘත්තයක් සම්බන්ධ ගැටලු විසඳීම. 2. වෘත්තයක් යනු, මධ්‍යස්ථානයක සිට සෑම ලක්ෂ්‍යයක් දක්වා දුර සමාන වන ලක්ෂ්‍යයන්ගේ සමුහයකි.

1. **Stating the problem:** We will explain the concept of geometric construction and solve an example: constructing the perpendicular bisector of a line segment. 2. **What is geom

1. **State the problem:** We have two right triangles. The smaller triangle has legs 14 and 8 units. The larger triangle has legs 21 and 12 units, and a hypotenuse of 24 units. We

1. **State the problem:** We have two right triangles. The first triangle has legs 14 and 8 units. The second triangle has legs 21 and 12 units, and the hypotenuse is labeled 24 un

1. The problem is to find the image of point $A=(-1,0)$ after reflection on the $y$-axis. 2. Reflection on the $y$-axis changes the $x$-coordinate of a point to its opposite, while

1. **State the problem:** We have a sector OAB of a circle with central angle $131^\circ$ and arc length $192$ cm. We need to find the radius $r$ of the circle. 2. **Recall the for

1. **State the problem:** We have a sector OAB of a circle with a central angle of $131^\circ$ and an arc length of 192 cm. We need to find the radius $r$ of the circle to 2 decima

1. **State the problem:** We have a circle with center $P$ and points $A, B, C, D, E$ on the circle in clockwise order. $\overline{AD}$ and $\overline{BE}$ are diameters. We want t

1. **State the problem:** We need to find the surface area of a triangular prism with triangle sides 26 yd and 19 yd, prism height 10 yd, and base length 24 yd. 2. **Identify the s

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 8 ft and 12 ft, and legs of 18 ft and 4 ft. 2. **Identify the bases and height:** The two pa

1. **State the problem:** We have a rectangular prism storage container with dimensions 7 m, 5 m, and 2 m. The total cost of the sheet steel used for the surface area is 4484. We n

1. **State the problem:** We have a kite WXYZ with diagonals XZ and WY intersecting at V. Given that $XZ = 18$ and $WY = 52$, and the sides WX, XZ, WY are labeled as follows: $XZ =

1. The problem asks if there is a way to solve geometry problems without using similar triangles. 2. Similar triangles are often used because they allow us to find unknown lengths

1. **State the problem:** We need to calculate the length of segment $FG$ in the given geometric figure. 2. **Analyze the figure:** We have a right triangle $DEF$ with right angle

1. **State the problem:** We are given three angles formed by intersecting lines with expressions $(8x - 10)^\circ$, $(6y + 20)^\circ$, and $(7x)^\circ$. We need to find the values

1. **State the problem:** We are given three angles formed by two parallel lines and a transversal: \( (8x - 10)^\circ \), \( (7x)^\circ \), and \( (6y + 20)^\circ \). We need to f