📐 geometry

1. **State the problem:** We have a rectangular pastry of width 37 cm and height 20 cm with eight circles cut out. Each circle has a diameter of 8 cm. We need to find the area of t

1. **Problem Statement:** Calculate the area of each shaded shape.

1. **Problem statement:** Calculate the area of each compound shape described, including estimates and precise areas to specified decimal places.

1. **Problem 10:** A rancher has a scale drawing of a horse stable with scale 1 inch = 3 feet. The drawing shows a rectangle 15 inches by 30 inches. Find the actual area in square

1. Problem 10: Calculate the area in square feet of a horse stable from a scale drawing. - Given scale: 1 inch = $3^2 = 9$ feet.

1. **Problem:** Ellie has a triangular island with an original area of 12 cm² using a wrong scale. The scale factor is enlarged to 3 cm. Find the new area. 2. **Formula:** Area sca

1. **Problem:** Calculate the area of a triangle with base 6 cm and height 4 cm, then scale it by a factor of 3 squared. 2. **Formula:** Area of a triangle is given by $$\text{Area

1. **Problem 1: Square Box Area Increase** Jordan's wooden box is a square with side length 6 cm. He increases each side by 1.6 cm.

1. **Problem statement:** Given parallelogram MNPQ, with MR = $2x + 14$ and MP = $8x - 12$, solve for $x$ and find the length of $RP$. 2. **Key property:** In a parallelogram, the

1. **State the problem:** We are given an equilateral triangle $\triangle TUV$ with points $X, Y, Z$ inside it forming smaller triangles. We need to complete the proof by ordering

1. **State the problem:** We have a parallelogram ABCD with sides AB, BC, CD, and AD given as expressions in terms of variables $x$ and $y$: - $AB = 4y - 17$

1. **State the problem:** We have a parallelogram ABCD with sides given as $AB=4y-17$, $BC=y+2$, $CD=3x+12$, and $AD=2x+3$. We need to find the values of $x$, $y$, and the lengths

1. **Problem Statement:** Given that ABCD is a parallelogram, we want to understand the properties and implications of this statement. 2. **Definition and Properties:** A parallelo

1. **Problem Statement:** We have a square with vertices at $(-1,1)$, $(3,1)$, $(3,-3)$, and $(-1,-3)$, and circles defined by equations such as $(x+1)^2+(y-1)^2=4$, $(x-1)^2+(y+1)

1. **Problem Statement:** We have a square with vertices at $(-1,1)$, $(3,1)$, $(3,-3)$, and $(-1,-3)$ in the $xy$-plane. A circle is tangent to all four sides of this square. We n

1. **State the problem:** Determine the most descriptive name for quadrilateral PQRS using the slope and distance formulas.

1. **State the problem:** Safana has a right rectangular prism with edge lengths $3 \frac{1}{2}$ ft, $2 \frac{1}{4}$ ft, and $4 \frac{1}{3}$ ft. She wants to fill it completely wit

1. **Problem statement:** We have a triangle with interior angles 18°, x°, and an exterior angle of 66° adjacent to the angle x°. We need to find the value of x. 2. **Key concept:*

1. **Problem statement:** We have a triangle with an exterior angle of 66° formed by extending one side. Inside the triangle, one angle is 18° and the angle opposite the exterior a

1. **Problem statement:** We have a triangle with an interior angle $18^\circ$, another interior angle $x^\circ$, and an exterior angle adjacent to $x$ measuring $66^\circ$. We nee

1. **Problem statement:** We have a triangle with an exterior angle of 76° formed by extending one side. Inside the triangle, two angles are given: $x^\circ$ and 51°. We need to fi