📐 geometry

1. **State the problem:** Find the area of a compound figure composed of a tall rectangle with a semicircle on the top-right and a rectangular notch on the right side. 2. **Identif

1. The problem is to find the "omkreds" which is Danish for "perimeter" of a shape. 2. The perimeter of a polygon is the sum of the lengths of all its sides.

1. **Stating the problem:** Calculate the area of the step-like composite polygon composed of rectangles with side lengths labeled as $a$, $b$, and $3a$.

1. **Problem statement:** Ava is comparing two tilings: one with squares and one with regular hexagons. Each tile has an area of 140 cm².

1. The problem asks: After a 270° counterclockwise rotation about the origin, which triangle does triangle A map to? 2. Rotation rule: A 270° counterclockwise rotation about the or

1. The problem asks to find the translation vector that maps triangle ITR (preimage) onto triangle I'T'R' (image). 2. A translation vector \(\vec{v} = \langle x, y \rangle\) moves

1. **Énoncé du problème :** Justifier que les droites (MN) et (PQ) sont parallèles. 2. **Rappel de la propriété :** Deux droites sont parallèles si elles ont la même direction, c’e

1. **State the problem:** We need to find the length of the elevator path that goes up the incline of a lateral edge of a pyramid with a rectangular base of dimensions 80 m by 60 m

1. **Problem statement:** Draw a triangle and explain the Law of Cosines. 2. **Law of Cosines formula:** For a triangle with sides $a$, $b$, and $c$, and angle $\gamma$ opposite si

1. The problem asks: What characteristics does a point have in geometry? 2. In geometry, a point is defined as an exact location in space.

1. **State the problem:** We want to find how doubling the radius of a right cone affects its surface area. 2. **Formula for surface area of a right cone:**

1. **State the problem:** We have a right triangular prism with side lengths 5 in, 12 in, and 9 in. We want to find: (a) The length $a$, which is the diagonal across the triangular

1. **State the problem:** We have a tent shaped like an isosceles triangular prism. We need to find the length $a$ of the segment from the top front corner to the front bottom righ

1. **State the problem:** We have a rectangular prism birdcage with base side lengths 6 m and 8 m, and height 7 m. A branch of length $b$ stretches from one corner of the prism to

1. **Problem statement:** Square ABCD has side length 3 cm. Points M and N lie on sides AD and AB respectively such that segments CM and CN divide the square into three regions of

1. **State the problem:** We are given six angles around a point: $(g-86)^\circ$, $(6f)^\circ$, $45^\circ$, $15^\circ$, $(e-27)^\circ$, and $d^\circ$. We need to find the value of

1. **State the problem:** We have a right triangle with hypotenuse length 11 units and one leg length 5 units. We need to find the length of the other leg. 2. **Formula used:** In

1. **State the problem:** We have a cylinder of height 15 cm with a hemisphere removed from the top such that the bottom of the hemisphere touches the center of the base of the cyl

1. The problem asks to find the surface area of a solid given the base area $B=144$ mm² and lateral area $L=1800$ mm². 2. The formula for the total surface area $S$ of a solid is:

1. The problem asks which equation correctly represents the surface area of a figure composed of two cubes, one with side length 5 cm and the other with side length 3 cm placed on

1. The problem asks for the expression representing the total surface area of a rectangular prism with dimensions 5 cm, 4 cm, and 7 cm. 2. The formula for the total surface area $S