📐 geometry

1. **Problem statement:** Given $m \angle JKM = 100^\circ$, $m \angle NKM = 29^\circ$, and $\overline{KN}$ bisects $\angle LKM$, find $m \angle JKL$. 2. **Understanding the problem

1. **Problem statement:** We need to find the total amount of paint required to paint the top hemispherical part of 3000 Bosu exercise balls. Each ball's top is a hemisphere with a

1. **Problem 16:** Find the height of a right pyramid with volume 72 m³ and base dimensions 800 cm by 300 cm. 2. **Formula:** The volume $V$ of a pyramid is given by $$V = \frac{1}

1. **State the problem:** We have a cylinder with height 24 feet and radius 2 yards. We need to find:

1. **State the problem:** We are given a circle with points P, Q, R, S, and T on its circumference. The angle \(\angle SQR = 52^\circ\) and the angle \(\angle PRT = 16^\circ\). We

1. **Problem Statement:** Find the volumes of the given shapes based on the provided dimensions. 2. **Formulas and Rules:**

1. **Problem statement:** Find the volume of the triangular pyramid (tetrahedron) with a right triangle base of legs 9 km and 9 km, and a height of 11 km. 2. **Formula:** The volum

1. **Problem Statement:** Find the length of the line segment NO where N = (4,0) and O = (12,0) in a square space of dimensions $2a \times 2a \times 2a$.

1. **Problem statement:** We have a right triangle with sides 13, 14, and 15 units, and a semicircle inside the triangle with its diameter along the side of length 14. We need to f

1. **Problem Statement:** Calculate the surface area of the following 3-D objects to the nearest hundredth. ---

1. **Problem statement:** We have a regular octagon ABCDEFGH with center O. We need to calculate the size of angle $AOB$, where $A$ and $B$ are adjacent vertices and $O$ is the cen

1. **Stating the problem:** We have a tetrahedron with edges labeled in terms of $a$ and constants. We need to find the value of $a$ given the edge lengths. 2. **Understanding the

1. **State the problem:** We have a rectangle with a length of 210 inches and an area of 43 3/4 square feet. We need to find the width in inches. 2. **Convert the area to square in

1. **State the problem:** We have a garden consisting of a rectangle 18.4 feet long and 8.6 feet wide, with two semi-circles on the shorter ends. We need to find:

1. **Problem statement:** We have two similar triangles and need to find the values of $x$ and $y$ using proportions. 2. **Understanding similarity:** Similar triangles have corres

1. Stwierdzenie problemu: W trójkącie ABC o polu $S$ na boku $AB$ wybrano punkt $D$ tak, że $\frac{|AD|}{|DB|} = p > 0$. Przez $D$ poprowadzono prostą równoległą do $AC$, przecinaj

1. Stwierdźmy problem: W trójkącie $ABC$ o polu $S$ na boku $AB$ wybrano punkt $D$ taki, że $|AD|=\frac{p}{p+1}|AB|$, gdzie $p>0$. Przez $D$ poprowadzono prostą równoległą do $AC$,

1. **State the problem:** We are given two trapezoids with side lengths and asked to verify if they are similar. 2. **Recall the similarity rule for trapezoids:** Two trapezoids ar

1. Stwierdzenie problemu: W trójkącie $ABC$ o polu $S$ na boku $AB$ wybrano punkt $D$ tak, że $\frac{|AD|}{|DB|}=p>0$. Przez $D$ poprowadzono prostą równoległą do $AC$, przecinając

1. Stwierdzenie problemu: Mamy trójkąt $XYZ$ o polu $S$. Na boku $XY$ wybrano punkt $P$ tak, że $\frac{|XP|}{|PY|}=q>0$. Przez $P$ poprowadzono prostą równoległą do $YZ$, przecinaj

1. Stwierdzenie problemu: W trójkącie $ABC$ o polu $S$ na boku $AB$ wybrano punkt $D$ tak, że $\frac{|AD|}{|DB|}=p>0$. Przez $D$ poprowadzono prostą równoległą do $AC$, przecinając