📐 geometry

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

1. **State the problem:** We have triangle UVW with angles at V and W given as $110^\circ$ and $2.3^\circ$ respectively, and side UV = 6. We need to find side $v = UW$. 2. **Find t

1. **State the problem:** Calculate the surface area of a triangular prism given the net with dimensions. 2. **Identify the shapes in the net:** The net includes:

1. **State the problem:** We need to find the surface area of a triangular prism given its net with dimensions. 2. **Identify the shapes in the net:** The net consists of:

1. **State the problem:** We are given the circumference of a circle as 11.304 inches and need to find the circle's diameter and radius. 2. **Formula used:** The circumference $C$

1. **State the problem:** Find the circumference and area of a circle with radius $r = 8.9$ cm. 2. **Formulas:**

1. **State the problem:** We need to find the length of the hypotenuse of a right triangle with legs measuring 6 ft and 8 ft. 2. **Formula used:** For a right triangle, the Pythago

1. **Problem statement:** Given a quadrilateral ABCD inscribed in circle O, BD is the perpendicular bisector of OC. On AD, point P is taken such that $OP=R$ (radius of circle O). L

1. **State the problem:** Find the surface area of the composite figure consisting of a rectangular prism and a triangular prism on top. 2. **Identify dimensions:**

1. **State the problem:** Find the surface area of a rectangular prism with length $15$ cm, height $7$ cm, and width $5$ cm. 2. **Formula:** The surface area $S$ of a rectangular p

1. **State the problem:** We need to find the length of the hypotenuse $x$ in a right triangle $MNO$ where the right angle is at $N$, the leg $NO$ is 7 units, and the angle at $O$

1. **State the problem:** We have a right triangle $\triangle KLM$ with $\angle M = 90^\circ$, sides $KM = 48$, $ML = 55$, and hypotenuse $LK = 73$. We want to find the ratio that

1. **Problem statement:** We have a trapezium with parallel sides of lengths $4p$ (top) and $3q$ (bottom), and a height of $6p$. The area is given as 750 square units. 2. **Formula

1. **State the problem:** We need to find the diameter of a circle given its radius. 2. **Formula:** The diameter $d$ of a circle is twice the radius $r$. This is expressed as:

1. **State the problem:** We need to find the diameter of a circle given its radius. 2. **Formula:** The diameter $d$ of a circle is twice the radius $r$. This is expressed as: