📐 geometry

1. **State the problem:** We have two rectangles, KLMN and K'L'M'N', where K'L'M'N' is a dilation of KLMN. We need to find the scale factor of this dilation. 2. **Recall the formul

1. **Problem Statement:** A sheet of A4 paper (297mm x 210mm) is folded once and then laid flat on the table. We need to determine which of the given shapes could not be made by fo

1. **State the problem:** We need to find how many quarts of paint are required to paint the ramp with two coats, excluding the bottom. 2. **Identify the surface area to be painted

1. **State the problem:** We need to find the area of a triangle with a base of 20 meters and an altitude (height) of 45 meters. 2. **Formula for the area of a triangle:**

1. **State the problem:** We need to find the area of a triangle given the base and height measurements. 2. **Formula:** The area $A$ of a triangle is given by the formula:

1. **Énoncé du problème :** Boris dispose de planches de bois d'une surface totale de 1137,5 cm².

1. **Énoncé du problème** : Trouver les coordonnées du point B sachant que le point A a pour coordonnées $A(3,4)$, la distance entre A et B est $12$ unités, et la pente de la droit

1. **State the problem:** We have a quadrilateral with angles labeled as $ (8x - 7)^\circ $, $ (7x + 2)^\circ $, $ (10x)^\circ $, and $ 165^\circ $. We need to find the value of $x

1. **State the problem:** We have a quadrilateral with angles labeled as follows: top-left angle is $10x - 6$ degrees, top-right angle is 109 degrees, bottom-right angle is 79 degr

1. **State the problem:** We have a rectangular prism box with a base measuring 4 feet by 5 feet and a total surface area of 148 square feet. We need to find the height of the box.

1. **State the problem:** We are given two triangles sharing vertex $G$, with $HI \parallel EF$. Given lengths are $EF=4$, $HI=3$, $GF=5.6$, and $EG=4.8$. We need to find the lengt

1. **State the problem:** We have triangle VTU with WX parallel to TU. Given lengths are $VU=7.2$, $WV=5$, and $TW=4$. We need to find the length of $VX$. 2. **Use the properties o

1. **State the problem:** We are given a cylinder with two circular bases, each having an area of 706.5 m², and a height of 55 m. We need to find the total surface area of the cyli

1. **State the problem:** Find the surface area of a triangular prism with given dimensions: triangle base sides 10 m, 10 m, and 6 m, and prism length 16 m. 2. **Formula:** Surface

1. **Problem statement:** Find the measure of angle $a$ in a right triangle where the hypotenuse is 9.8 cm and the adjacent side to angle $a$ (bottom side) is 5.3 cm. 2. **Formula

1. The problem asks to identify the unknown angle $x$ and name the congruent pair for each diagram. 2. For part (a), the unknown angle is given as $x = 115^\circ$.

1. **Problem:** In a pentagonal garden, the exterior angle at one corner measures 50°. Find the interior angle at that corner. 2. **Problem:** In a decagonal plaza, the exterior an

1. **State the problem:** We have a right triangle LMN with a right angle at M. 2. **Identify the sides:** The sides are LM = 12, MN = 9, and LN = 15.

1. **Stating the problem:** We need to find the measure of angle $R$ in a given geometric figure. 2. **Formula and rules:** To find an unknown angle in a triangle, we use the fact

1. **Problem statement:** We have triangle MNR with angle $M = 120^\circ$, side $MN = 9$, side $NR = 16$, and we need to find angle $x = \angle R$. 2. **Formula used:** Use the Law

1. **State the problem:** Calculate the area of the triangles outlined by dotted lines. 2. **Formula for the area of a triangle:** The area $A$ of a triangle is given by