📐 geometry

1. Tehtävä: Selvitä puolisuunnikkaan yhdensuuntaisten sivujen pituudet, kun pinta-ala on 105 m², sivujen välinen etäisyys (korkeus) on 9,2 m ja toinen sivuista on 4,8 m pidempi kui

1. The problem states that the circle is divided into four sectors with angles 18°, $x$, $2x$, and 147°. 2. Since the total angle around a point in a circle is 360°, the sum of all

1. **State the problem:** We are given that $y = 4x$ and that angles $x$ and $y$ are adjacent angles on a straight line. 2. **Understand the relationship:** Adjacent angles on a st

1. The problem asks to find the measures of angles $\alpha$ and $\beta$ in a regular octagon, where the polygon has 8 equal sides and equal interior angles. 2. First, recall the fo

1. **Problem Statement:** Given a net of a cuboid with points labeled including point X, determine which two points will join with point X when the net is folded into the cuboid. 2

1. The problem asks for the number of vertices of a 3-D shape formed by folding a given 2D net. 2. The net described is a cube net, consisting of 6 squares arranged in a cross shap

1. **Stating the problem:** We have a parallelogram with angles labeled $\alpha$, $\beta$, $\gamma$, and one angle given as $108^\circ$. The side length at the bottom is $11$, the

1. The problem asks for the number of edges in a square-based pyramid once it is built. 2. A square-based pyramid consists of a square base and four triangular faces meeting at a s

1. The problem asks to match the given geometric terms to the correct shapes based on their properties. 2. Let's review the terms and their meanings:

1. Problem: Find two possible values for $k$ given the distance between points $(5, 2)$ and $(4, k)$ is $\sqrt{2}$. 2. Formula: The distance between two points $(x_1, y_1)$ and $(x

1. **State the problem:** We have two similar triangular prisms with corresponding side lengths. The smaller prism has sides 3 mm, 5 mm, 6 mm, and an unknown side $x$ mm. The large

1. **State the problem:** We have two similar trapezoidal prisms with corresponding linear dimensions. We need to find the unknown depth $x$ of the smaller prism. 2. **Identify cor

1. **Stating the problem:** We have a triangle with two sides measuring 126 m and 100 m, and the included angle between these sides is 75°. We want to find the length of the third

1. **Problem Statement:** Given that triangle ABC is congruent to triangle EDF, Priya knows there is a sequence of rigid motions that maps ABC to EDF. We need to determine which st

1. **Problem statement:** We need to find the length of segment $AB$ in a triangular prism where $FE=8$ cm, $EC=14$ cm, the angle at vertex $F$ between edges $FA$ and $FB$ is $23^\

1. **Problem statement:** We have a triangular prism with given lengths: DE = 22 mm, CD = 15 mm, CF = 9 mm.

1. **State the problem:** We have two similar rectangles, A and B. Rectangle A has an area of 39 and width 13. Rectangle B has width 4.55, and we need to find its area.

1. **State the problem:** We have a right triangle with sides 14, 11, and $x$, where $x$ is the side opposite the right angle. We need to find the value of $x$. 2. **Formula used:*

1. The problem asks which sets of three lengths can form a right triangle. 2. To determine if three lengths $a$, $b$, and $c$ form a right triangle, we use the Pythagorean theorem:

1. **State the problem:** We need to find the values of $w$, $x$, and $y$ in a parallelogram where the sides are labeled as follows: - Side AB: $x + 16$

1. **Problem statement:** Given kite RSTU with angles labeled as $m\angle R = x + 30^\circ$, $m\angle T = x^\circ$, and $m\angle U = 125^\circ$, and sides RS = RU and ST = UT, find