📐 geometry

1. **State the problem:** We have a figure with squares ABCD, DCEF, and FEPQ, and we want to find the sum of the lengths CAQ + EAQ + PAQ. 2. **Understand the problem:** Each of the

1. **State the problem:** We need to find the horizontal distance between two skyscrapers given the angle of inclination from the base of skyscraper A to the top of skyscraper B is

1. **State the problem:** Find the measure of NK in a circle where one leg is 9, the hypotenuse is 15, and the other leg is unknown (NK). 2. **Formula used:** Use the Pythagorean t

1. **Тодорхойлолт:** Өнцгийн хэмжээг транспортираар хэмжихэд өнцгийн хоёр талын хоорондох өнцгийн хэмжээг градусаар илэрхийлнэ. 2. **Формул ба дүрэм:** Өнцгийн хэмжээг градусаар хэ

1. **State the problem:** Find the surface area of a rectangular prism with dimensions height $h=3$ yd, width $w=5$ yd, and depth $d=1 \frac{1}{5}$ yd. 2. **Convert mixed number to

1. **State the problem:** We need to find the volume of a rectangular prism with dimensions height = 3 yards, length = 5 yards, and width = 1 \frac{1}{5} yards. 2. **Formula:** The

1. **State the problem:** We need to find the area of a right triangle with a base of 4 inches and a height of 3 inches. 2. **Formula:** The area $A$ of a triangle is given by the

1. **State the problem:** Find the area of a triangle with sides 7 mm, 6 mm, and 5 mm, where the 5 mm side is perpendicular to the base. 2. **Formula for the area of a triangle:**

1. **State the problem:** Given that line segment $\overline{AB}$ is parallel to line segment $\overline{DE}$, prove that triangle $\triangle ABC$ is similar to triangle $\triangle

1. The problem is to understand and use the formula for the volume of a sphere, which is given by $$V = \frac{4}{3} \pi r^3$$ where $V$ is the volume and $r$ is the radius of the s

1. **State the problem:** We have two triangles side by side with given side lengths. We need to find the length $x$ of the hypotenuse of the right triangle. 2. **Identify the tria

1. **Problem statement:** We have a circle with center $O$ and radius $OA = 7.5$ cm. The radius $OA$ is perpendicular to chord $AB$. Point $D$ lies on the circle such that $\angle

1. **Problem Statement:** Find the area of a regular hexagon with side length 10 inches. 2. **Formula:** The area $A$ of a regular polygon with $n$ sides of length $s$ can be found

1. The problem asks to find the area of a regular pentagon with a perimeter of 50 cm. 2. Recall the formula for the area of a regular polygon: $$\text{Area} = \frac{1}{2} \times \t

1. **State the problem:** Find the area of an oval (ellipse) with a vertical height of 15 ft and a horizontal width of 4 ft. 2. **Formula for the area of an ellipse:**

1. **Problem Statement:** Find the area of the triangles in exercises 7 and 9. ---

1. **State the problem:** We need to determine the values of the angles $a^\circ$, $b^\circ$, and $c^\circ$ shown in the graph around the origin in the Cartesian coordinate system.

1. **State the problem:** We need to find the area of an L-shaped lot with given side lengths: top horizontal segment = 30 m, right vertical segment = 9 m, bottom horizontal segmen

1. **State the problem:** Find the area of the composite figure consisting of a rectangle and a trapezoid on top. 2. **Identify dimensions:**

1. The problem asks to identify the correct position to mark a bearing of 235° from point X using a protractor. 2. Bearings are measured clockwise from the north direction (0°).

1. **State the problem:** We are given the area of a rectangle as 28 m² and the width as 3.2 m. We need to find the length and the perimeter of the rectangle. 2. **Formula for area