📐 geometry

1. **State the problem:** We need to find the total surface area of a solid hemisphere with radius $8$ cm. 2. **Recall the formulas:**

1. The problem asks to find the circumference of a circle with a diameter of 158 cm, rounded to 1 decimal place. 2. The formula for the circumference $C$ of a circle is:

1. The problem asks for the circumference of a circle with a diameter of 13 cm. 2. The formula for the circumference $C$ of a circle is given by:

1. **Problem statement:** Find the following:

1. **Problem statement:** We need to find the length of the diagonal $DG$ inside the cuboid. 2. **Given dimensions:**

1. The problem asks for the degree of rotation that maps a regular hexagon onto itself when rotated about its center. 2. A regular hexagon has 6 equal sides and 6 equal angles.

1. **State the problem:** Find the perimeter of rectangle PQRS with vertices P(4,1), Q(4,7), R(8,7), and S(8,1). 2. **Recall the formula for perimeter of a rectangle:**

1. The problem asks to identify all triangles similar to triangle T from the given shapes A, B, C, D, E, and F. 2. Two triangles are similar if their corresponding angles are equal

1. **Problem Statement:** Identify which two shapes among A, B, C, D, E, and F are similar based on their geometric properties. 2. **Understanding Similarity:** Two shapes are simi

1. **State the problem:** We need to find which two triangles among A, B, C, D, and E are congruent based on their side lengths. 2. **Recall the congruence rule for right triangles

1. The problem asks to identify which two shapes among A, B, C, D, E, F, and G are congruent. 2. Congruent shapes have the same size and shape, meaning their corresponding sides an

1. **State the problem:** We have a square window with area 81 cm², so each side is $\sqrt{81} = 9$ cm.

1. **Problem statement:** Given a pyramid $S.ABCD$ with base $ABCD$ a trapezoid where $AB \parallel CD$. Point $E$ lies on segment $SA$. Plane $(P)$ passes through $E$ and is paral

1. **Problem statement:** Given a rectangular prism ABCD.A'B'C'D', a plane parallel to the side ABB'A' intersects edges AD, BC, A'D', B'C' at points M, N, M', N' respectively.

1. The problem asks which triangle among A, B, C, D, E, and F is similar to triangle T. 2. Two triangles are similar if their corresponding angles are equal and their corresponding

1. **State the problem:** Find the midpoint coordinates of points P(4, 3) and Q(10, 9). 2. **Formula:** The midpoint $M$ of two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is given by:

1. সমস্যাটি হলো: একটি বৃত্তের কেন্দ্র O এবং ব্যাসার্ধ 10 সেমি। AB একটি chord যার দৈর্ঘ্য 14 সেমি। কোণ AOB এর মান রেডিয়ান এককে নির্ণয় করতে হবে। 2. সূত্র: বৃত্তের কেন্দ্র O থেকে ch

1. **State the problem:** Calculate the area of a right triangle with legs measuring 5 cm and 8 cm. 2. **Formula:** The area $A$ of a right triangle is given by

1. **State the problem:** We need to find the area of the dotted blue triangle inside a rectangle with width 6 cm and height 4 cm. 2. **Formula for the area of a triangle:** The ar

1. **State the problem:** We have a right triangle with legs measuring 5 cm and 17 cm. We need to find the length of the hypotenuse. 2. **Formula used:** The Pythagorean theorem st

1. **State the problem:** We have a rectangle with an area of 99 square units and a width of 11 units. We need to find the length of its diagonal, rounded to the nearest tenth. 2.