📐 geometry

1. **State the problem:** Calculate the perimeter of a sector of a circle with radius $3.5$ cm and central angle $35^\circ$. 2. **Formula for perimeter of a sector:**

1. The problem asks whether adjacent angles can be supplementary. 2. Adjacent angles are two angles that share a common side and a common vertex.

1. **State the problem:** We have a triangular prism with a triangular base having sides 6 in, 8 in, and 10 in, and the prism height (length) is 12 in. We need to find the volume a

1. **State the problem:** We have a stick 0.5 m high casting a shadow 1.25 m long, and a tree casting a shadow 10 m long. We need to find the height of the tree using similar trian

1. The problem asks to find the missing angle $x$ in a triangle where the other two angles are $85^\circ$ and $45^\circ$. 2. Recall the Triangle Angle Sum Theorem: The sum of the i

1. **Stating the problem:** We need to find the total surface area of the composite 3D solid shown, which consists of a rectangular prism with a slanted roof.

1. **Nêu bài toán:** Cho hai hình chóp tứ giác đều có cạnh đáy và chiều cao đều bằng 8 cm, được xếp chồng lên nhau như hình vẽ. Hai điểm P và M chia đường chéo của hình chóp theo t

1. **State the problem:** We need to find the cotangent of angle $\angle S$ in right triangle $RQS$ where $\angle R$ is the right angle. 2. **Given sides:**

1. Bài toán yêu cầu chứng minh hai tam giác đồng dạng. 2. Để chứng minh tam giác đồng dạng, ta có thể sử dụng các tiêu chuẩn đồng dạng tam giác như:

1. **Nêu bài toán:** Từ điểm A ở ngoài đường tròn (O), kẻ hai tiếp tuyến AB và AC tới đường tròn, B và C là các tiếp điểm. Đường thẳng d đi qua A cắt đường tròn (O) tại hai điểm E

1. The problem asks to find the area of the shaded region in the shop plan, which is a large rectangle with a smaller rectangular section cut out from the top-left corner. 2. To fi

1. **State the problem:** We need to estimate the volume of a cylinder-shaped blob of toothpaste with length (height) $h = 0.75$ cm and diameter $d = 0.5$ cm. 2. **Formula:** The v

1. **State the problem:** We need to find the surface area of a triangular prism using its net. 2. **Given:** Each triangular face has a base of 10 cm and a height of 8 cm. There a

1. **State the problem:** We need to find the surface area of a rectangular prism using its net. 2. **Given dimensions and areas:**

1. The problem asks to identify the mistake in Florence's description of the translation from shape A to shape B and to find the correct translation vector. 2. A translation moves

1. **State the problem:** We need to find the size of angle $q$ at the top apex of a concave polygon. 2. **Recall the polygon angle sum rule:** The sum of the interior angles of an

1. **Problem Statement:** We are given a quadrilateral with side lengths 9, 18, 18, and 9, and it is described as a rectangle with four right angles. 2. **Recall the properties of

1. **State the problem:** We have a right triangle with one leg measuring 12 centimeters, the hypotenuse measuring 19 centimeters, and the other leg unknown. We need to find the mi

1. The problem asks for the area of compound figures, but only four shapes are described without a specific question 6. 2. Since no question 6 is provided, I cannot solve it.

1. **Nyatakan masalah:** Kita perlu mengira isipadu gabungan pepejal yang terdiri daripada sebuah kuboid dan sebuah silinder tegak. 2. **Diberi:**

1. **Stating the problem:** We are given an equilateral triangle PQT and a quadrilateral T-S-R-Q with given angles 140° at P, 80° at S, and 130° at R. We need to find the value of