📐 geometry

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

1. **Problem Statement:** Moira walked 3.5 km west and then 4.5 km north from her house. We need to find the straight-line distance from her current position back to her house. 2.

1. **Stating the problem:** We have a right triangle \(\triangle ABC\) inscribed in a circle where \(CA\) is the diameter. We need to identify the hypotenuse, adjacent, and opposit

1. **Problem Statement:** Calculate the area of a hexagonal sun deck with a top side length of 40 cm, a bottom side length of 96 cm, and a vertical height of 90 cm. 2. **Formula Us

1. **הבעיה:** נתון מעוין ABCD ונקודה M על האלכסון AC כך ש- MD = MC. 2. **הוכחת M מרכז המעגל החוסם את המשולש DBC:**

1. Problem: Find the number of things which coincide with one another. 2. The question asks: "The things which coincide with one another are?" with options a)0 b)1 c)2 d)3.

1. **State the problem:** We have a larger square with side length 18 cm and a smaller square carpet inside it with side length 9 cm. The carpet is centered, and there is a 1 cm ma

1. **State the problem:** We need to find the depth of the water in a rectangular cuboid container given the volume of water in milliliters (ml). Since 1 ml = 1 cm³, the volume of

1. **State the problem:** We need to find the volume of a cuboid with given dimensions. 2. **Given:**

1. **Problem:** Two similar triangles have the ratio of their corresponding sides as 3:4. Find the ratio of their areas. 2. **Formula and Rules:**