📐 geometry

1. **Problem statement:** We are given a trapezium with one side length 14.9 cm, bottom left angle 75°, bottom right angle 50°, and we need to find the length $r$ of the slant righ

1. **State the problem:** Calculate the area of a composite shape made of a rectangle and a right triangle on top. 2. **Identify dimensions:** Rectangle width = 6 cm, height = 10 c

1. **State the problem:** We need to find the area of a trapezium with height 4 cm, bottom base 10 cm, and a top left segment of 3 cm. The trapezium has right angles at the top rig

1. **State the problem:** We need to find the surface area of a rectangular prism with dimensions 14 cm (height), 6 cm (depth), and 4 cm (width).

1. The problem involves understanding the areas of rectangles given as 236 cm^2, 3000 cm^2, 328 cm^2, and 164 cm^2. 2. The area $A$ of a rectangle is calculated by the formula $$A

1. **State the problem:** We need to find the surface area of a triangular pyramid where each face is a congruent triangle with base $7$ ft and height $0.6$ ft. 2. **Formula for th

1. **State the problem:** We need to find the surface area of a rectangular prism with dimensions 10 m, 10 m, and 15 m. 2. **Formula for surface area of a rectangular prism:**

1. **State the problem:** We need to find the total surface area of a rectangular prism with dimensions 8 ft, 7 ft, and 5 ft. 2. **Formula for total surface area of a rectangular p

1. The problem asks for the surface area of a cube with side length 15 inches. 2. The formula for the surface area $S$ of a cube with side length $a$ is:

1. **State the problem:** We need to find the surface area of a cube with side length 4 cm. 2. **Formula:** The surface area $S$ of a cube with side length $a$ is given by:

1. The problem asks which triangle is correctly labeled with respect to the angle of 64° in a right triangle. 2. In a right triangle, the hypotenuse is always opposite the right an

1. **State the problem:** We need to find the perimeter of triangle $\triangle XYZ$ where two sides are given as 34.4 and 36, and the third side $x$ is unknown. The angles given ar

1. **State the problem:** We have a sphere of radius $R=18$ cm and a right circular cone inscribed inside it with height $h$ and base radius $r$. We want to find the maximum volume

1. **Problem 1: Calculate the round trip distance Michelle traveled on her motorcycle.** Given: Triangle with sides 45 miles and 32 miles, and included angle 70° between them.

1. **State the problem:** Find the distance between the points $(-6,5)$ and $(-3,7)$. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given

1. **State the problem:** We need to find the perimeter of a right-angled triangle where one angle is 43° and the side adjacent to this angle (the base) is 13.8 m. 2. **Identify kn

1. The problem asks if the point $(-5,0)$ lies on circle $Q$ centered at the origin $(0,0)$ with radius 5. 2. The formula for a circle centered at the origin is $$x^2 + y^2 = r^2$$

1. **State the problem:** We need to find the area of the trapezoid with sides 6.4 cm (top), 7.6 cm (bottom), 4.2 cm (left vertical), and 4.4 cm (right diagonal), with a right angl

1. **State the problem:** We have a parallelogram ABCD with angles labeled as follows: \(\angle A = 65^\circ\), \(\angle B = x^\circ\), \(\angle C = y^\circ\), and \(\angle D = z^\

1. The problem asks for the direct distance from home plate to second base on a baseball diamond, which is a square with sides of 90 feet. 2. To find the direct distance between tw

1. The problem asks to find the length of the walkway running diagonally through a rectangular garden with sides 15 ft and 24 ft. 2. To find the diagonal length of a rectangle, the