📐 geometry

1. **Stating the problem:** We are given a right triangle with sides labeled as follows: hypotenuse $5x + 11$, one leg $5x - 4$, and the other leg $3x$. There is also a segment lab

1. **Problem:** Find the diagonal of a cube if each edge is 2. 2. **Formula:** The space diagonal $d$ of a cube with edge length $a$ is given by $$d = a\sqrt{3}$$ because the diago

1. **Problem statement:** Given a regular square pyramid PADIM with slant height $PR=10$ and base diagonal $12\sqrt{2}$, find the following: (a) Length $ID$

1. **State the problem:** We have a triangle with angles 51°, 86°, and two unknown angles labeled $x$ inside the triangle. We need to find the value of $x$. 2. **Recall the triangl

1. The problem appears to involve identifying or working with points labeled D', E', G', F' on a coordinate grid. 2. Since no explicit question is given, let's assume we need to fi

1. The problem is to find the image of triangle ABC after a 270° clockwise rotation about the origin. 2. The formula for a 270° clockwise rotation (which is equivalent to a 90° cou

1. **State the problem:** We have rectangle WXYZ with side XY = 10 units and diagonal XZ = 26 units. We need to find how much longer the perimeter of the rectangle is than the diag

1. **State the problem:** We need to find the surface area of the right triangular prism MNOPQR. 2. **Identify given dimensions:** The triangular base has sides MN = 14 in, PR = 17

1. **State the problem:** We have a triangle with a segment dividing the base into two parts: one part is 3 units, the other is $x$ units. The left side of the triangle is 8 units,

1. **State the problem:** Determine if the quadrilateral formed by points F(4,1), G(3,-1), H(-3,2), I(-2,4) is a rectangle using the distance formula. 2. **Recall the distance form

1. **State the problem:** We need to find the area of a trapezoid with a curved top side, where the bottom base is 15 mm, the height is 6 units, and the top side length is 10 units

1. The problem is to calculate the approximate area, but the shape or function is not specified. 2. To calculate area, we need to know the shape or the function defining the region

1. **Stating the problem:** We have two triangles, \(\triangle STU\) and \(\triangle SCB\), sharing a common vertex \(S\). We want to analyze or find relationships involving these

1. **Stating the problem:** We are given two triangles, \(\triangle JKL\) and \(\triangle VUT\), which are similar (\(\triangle JKL \sim \triangle VUT\)). We want to understand the

1. **Problem statement:** Given two parallel lines $\overline{LN}$ and $\overline{OQ}$, and a transversal intersecting them at points $M$ and $P$ respectively, with $m \angle LMK =

1. **State the problem:** We need to find the surface area of a cuboid with length $9$ m, width $12$ m, and height $4$ m. 2. **Formula for surface area of a cuboid:**

1. **State the problem:** Calculate the areas of faces A, B, and C on a cuboid with dimensions 2 m, 6 m, and 9 m. 2. **Identify the dimensions of each face:**

1. **State the problem:** We have a parallelogram ABCD with diagonals intersecting at E. The angle at vertex C inside the parallelogram is given as $13x - 16$ degrees, and the adja

1. **State the problem:** Calculate the area of an irregular polygon shaped like an "L" with given side lengths: vertical left side 10 in, top horizontal side 9 in, bottom horizont

1. The problem states that we have a square plot of land with an area of 81 m², and we need to find the length of one side of the square. 2. The formula for the area of a square is

1. The problem involves understanding the given expressions and their relationships. 2. We have $x = \frac{3}{6} \times 2$, which simplifies to $x = \frac{3}{6} \times 2 = \frac{3