📐 geometry

1. **State the problem:** Find the area of a trapezoid with top base $2$ km, height $2 \frac{1}{2}$ km, and bottom base $4 \frac{1}{3}$ km. 2. **Formula for the area of a trapezoid

1. The problem asks for the coordinates of point $Z(0, 2)$ after it is reflected over the x-axis. 2. Reflection over the x-axis changes the $y$-coordinate of a point to its opposit

1. **State the problem:** We need to find a series of transformations that map Figure R onto Figure S. 2. **Identify coordinates:** Approximate coordinates for Figure R are $(-9,-9

1. **State the problem:** Classify triangle $\triangle TUV$ by its sides and angles.

1. **State the problem:** Triangle JKL has vertices J(2,4), K(3,1), and L(3,3). A translation maps point J to J'(3,3). We need to find the coordinates of K' after the same translat

1. **State the problem:** We have a right triangle with legs measuring 6.6 yards and 6.4 yards. We need to find the perimeter, which is the sum of all three sides. 2. **Formula use

1. **State the problem:** We have a right triangle with one leg of length 7.5 yd, hypotenuse 9.3 yd, and the other leg labeled $a$. We need to find the perimeter, which is the sum

1. The problem asks to identify the transformation illustrated by the graph. 2. The graph shows two shapes: one in the top-left quadrant and one in the bottom-right quadrant.

1. **Problem:** Find the measure of angle $\angle YZV$ given arcs and angles in a circle. 2. **Formula:** The measure of an inscribed angle is half the measure of its intercepted a

1. **State the problem:** We are given trapezoid PQRS with vertices P, Q, R, S in clockwise order. Given: $m\angle P = 104^\circ$ and $m\angle R = 41^\circ$.

1. **Problem statement:** Find the measures of angles $m\angle WRZ$ and $m\angle XWY$ given that $m\angle H = (8x - 2)^\circ$ and the context involves trapezoids and quadrilaterals

1. **State the problem:** We have two similar quadrilaterals ABCD and FGHJ with a ratio of similitude (scale factor) of $7:11$.

1. **State the problem:** We have two similar triangles. The longest side of the first triangle is 8 less than 3 times the longest side of the second triangle. The shortest sides o

1. **State the problem:** We are given a circle with center $O$, a radius extending horizontally to the left, and an arc measuring $80^\circ$ from the end of this radius to a point

1. **Problem Statement:** Find the scale factor of the enlargement from triangle PQR to P'Q'R', explain why it is negative, find the length of P'Q', the area of triangle PQR, and t

1. **State the problem:** We are given triangles \(\triangle LMN\) and \(\triangle PQR\) with coordinates: - \(L(1,2)\), \(M(3,2)\), \(N(3,5)\)

1. **Problem:** Given square FGHI with perimeter 108 units, find the length of diagonal GI. 2. **Formula:** For a square with side length $s$, perimeter $P = 4s$.

1. **Problem Statement:** Find the area of the parallelogram shown in the coordinate plane. 2. **Formula:** The area $A$ of a parallelogram is given by:

1. **State the problem:** We have two similar trapezoids DEFG (original) and JKLM (new). We know the height of DEFG is 48 m and the height of JKLM is 12 m. The top base of JKLM is

1. **State the problem:** We have two similar rectangles ABCD and WXYZ. We know the length of ABCD is 35 inches and the length of WXYZ is 5 inches. The width of WXYZ is 3 inches, a

1. **Problem statement:** Given two lines and a ray intersecting to form five angles numbered 1 through 5, with \(\angle 4 = 55^\circ\), find the measure of \(\angle 2\). 2. **Unde