📐 geometry

1. **State the problem:** We have a large equilateral triangle formed by 4 identical smaller equilateral triangles. Each small triangle has area $25\sqrt{3}$. We are asked to find

1. **State the problem:** We have trapezium $ABCD$ with $AD \parallel BC$ and $\angle ADC = 90^\circ$. $M$ is midpoint of $AB$, $CM = \frac{13}{2}$ cm, and $BC + CD + DA = 17$ cm.

1. **State the problem:** We have triangle $ABC$ with sides $BC=17$, $CA=18$, and $AB=19$. Point $P$ has perpendiculars to the sides (or their extensions) $BC$, $CA$, and $AB'$ at

1. **State the problem**: We have a square ABCD with side length $2\sqrt{15}$. Points E and F are midpoints of sides AB and BC respectively. Points M and N lie on AE and BF, and we

1. **State the problem:** We have a square ABCD with side length $2\sqrt{15}$. Points E and F are midpoints of sides AB and BC respectively. We need to find the area of triangle $\

1. **Stating the problem:** We have a hexagon ABCDEF with conditions:\n- CD || AF\n- \(\angle CDE = \angle BAF\)\n- AB is perpendicular to BC (\(AB \perp BC\))\n- \(\angle E = 80^\

1. Let's state the problem: We know the lighthouse is 30 metres tall. 2. To find the height of the cliff, we typically need additional information such as total height or a relatio

1. **State the problem:** We are given the radius of a spherical balloon as 21 cm and need to calculate its volume. 2. **Recall the formula for the volume of a sphere:** The volume

1. The problem involves understanding the radius of a spherical balloon and potentially finding related properties like volume or surface area. 2. If the radius $r$ is given or can

1. The problem is to calculate the expression $\frac{4}{3} \times 3.14 \times 20 \times 20 \times 20$. 2. First, calculate the product of the terms inside the multiplication: $20 \

1. **Problem (c):** Find the leg $y$ of a right triangle with hypotenuse 13 cm and angle 25° opposite to $y$. 2. In a right triangle, the sine of an angle gives the ratio of the op

1. The problem asks to find formulas for points 8, 9, 10 related to cones, spheres, and hemispheres. 2. Based on Chapter 11.5 summary, points 1-7 are about surface areas and volume

1. The problem is to convert an angle given in degrees into Degrees, Minutes, and Seconds (DMS) format. 2. Start with the angle in decimal degrees, for example, $\theta = 45.7625^\

1. The problem is to convert various angles given in degrees and minutes or seconds to decimal degrees. 2. To convert degrees, minutes, and seconds to decimal degrees, use the form

1. The main task is to convert the given angles from decimal degrees to degrees, minutes, and seconds (DMS) format or verify the given DMS values, and possibly interpret the maze g

1. The problem is to find the volume of a pyramid given the height and base area. 2. First, note the given information:

1. **State the problem**: We have two spheres made of the same uniform rock. The first sphere has a radius of $4.50$ cm. The mass of the second sphere is five times the mass of the

1. The problem asks to find the bearing of point Y from point X given the angle relative to the north direction. 2. Bearing is measured clockwise from the north line, so if the ang

1. **State the problem:** Calculate the volume of a three-dimensional L-shaped prism with given dimensions. The volume is found by splitting the prism into two rectangular prisms a

1. Let's clarify the problem first: if you have a rectangle and you reorder or rearrange its dimensions, does it change its area or other properties? 2. The area of a rectangle is

1. Let's clarify that you meant a rectangle math question. 2. Please provide the exact rectangle question so I can help solve it step-by-step.