📐 geometry

1. **State the problem:** We need to find the area of a circular swimming pool with a diameter of 21 feet. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. **State the problem:** Find the area of a circle with radius $4$ meters. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. **State the problem:** We need to find the area of a circle with radius $r = 21$ ft. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. **State the problem:** We have a triangle with vertices A(-6, 5), B(-3, 4), and C(-3, 1). We want to find the image of this triangle after reflecting it over the y-axis. 2. **Fo

1. **State the problem:** We have a triangle with vertices A(1,7), B(4,7), and C(3,3). We want to find the coordinates of the reflected triangle across the line $y = x$. 2. **Refle

1. The problem states that a pre-image is located entirely in the second quadrant. 2. The second quadrant is where $x < 0$ and $y > 0$.

1. **State the problem:** We need to find the image of a triangle ABC under reflection across the x-axis. 2. **Recall the reflection rule:** Reflecting a point $(x,y)$ across the x

1. **State the problem:** We have a right triangle with one leg measuring 8 cm, the hypotenuse measuring 10 cm, and the other leg labeled as $x$. We need to find the length of $x$

1. **State the problem:** We need to find the distance between each pair of points given: (-4,-2), (-2,0), (0,2), (2,4), and (3,5). 2. **Formula used:** The distance $d$ between tw

1. **Problem statement:** We are given two circles where the difference of their circumferences is $4\pi$ and the difference of their areas is $24\pi$. We need to find the radii $r

1. **Stating the problem:** We need to find the surface area of the roof of a tower shaped like a rotational cone. 2. **Given data:** Radius of the base $r = 6$ m, height $h = 7$ m

1. The problem is to verify the surface area calculations of three rectangular prisms. 2. The formula for the surface area $SA$ of a rectangular prism with length $l$, width $w$, a

1. **State the problem:** We are given a circle with two lines from a common external point: one tangent and one secant. The angles formed are labeled as $(5x - 6)^\circ$, $3^\circ

1. **State the problem:** We have two secants intersecting outside a circle, forming an angle of $4x^\circ$. The intercepted arcs inside the circle are $35^\circ$ and $(9x + 26)^\c

1. **Problem Statement:** Find the areas of the sectors formed by \(\angle DFE\) given the total area and the central angle. 2. **Formula:** The area of a sector is given by

1. **State the problem:** We have a right rectangular prism with a shaded part inside it. The volume of the shaded part is 102 in³. We are asked to find the volume of the entire ri

1. **Problem:** Find the perimeter of the polygon with sides 8 in., 10 in., 7 in., and 11 in. 2. **Formula:** The perimeter $P$ of a polygon is the sum of the lengths of all its si

1. **Find m\angle Y in triangle ZXY** Given sides: \(ZX=24\), \(XY=13\), \(ZY=29\).

1. **Problem Statement:** Find the perimeter of the compound shape (i) with given dimensions in centimetres and using \(\pi = 3.14\). 2. **Understanding the shape:** The shape has

1. **Problem statement:** Find the area, arc length, and perimeter of the given sectors.

1. **State the problem:** We need to find the area of a right triangle with legs measuring 3 meters and 4 meters. 2. **Formula for the area of a triangle:**