📐 geometry

1. The problem states that the radius of a circle is 5. 2. We can find the circumference and area of the circle using the formulas:

1. The problem is to find the area of a half circle. 2. The formula for the area of a full circle is $$A = \pi r^2$$ where $r$ is the radius.

1. **Problem statement:** We need to find the size of angle $x$ in a right-angled triangle where the sides are given as 7.68 mm (opposite to $x$), 14.4 mm (adjacent to $x$), and 16

1. **Problem 1:** Given a triangle inside a circle with sides 8.8, x, and radius 22.4, find the value of $x$ from options A) 5, B) 4.3, C) 4.4, D) 3.1. 2. **Step 1:** Use the Pytha

1. The problem states that we have a circle and a scaled copy of the circle with a scale factor of 2. 2. We want to compare the area of the scaled copy to the area of the original

1. **State the problem:** Find the equation of the plane passing through points $P_1(1,2,-1)$, $P_2(2,3,1)$, and $P_3(3,-1,2)$.\n\n2. **Formula and concept:** The equation of a pla

1. সমস্যাটি হলো: ত্রিভুজ ADF এর ক্ষেত্রফল কত বর্গ সেন্টিমিটার? 2. প্রথমে, ত্রিভুজ ADF এর ক্ষেত্রফল নির্ণয়ের সূত্রটি মনে করি:

1. **Problem statement:** We have two similar triangles with sides 18 cm, 27 cm, 24 cm for the smaller triangle and sides x, y, 48 cm for the larger triangle. We need to find the v

1. The problem asks: How many degrees are in a straight line? 2. A straight line forms a straight angle.

1. The problem asks for the possible criteria for using the Law of Cosines. 2. The Law of Cosines is used to find unknown sides or angles in a triangle when you have:

1. **State the problem:** We have triangle $\triangle FGH$ with $IJ$ as a midsegment parallel to side $FG$. Given $IJ=11$, $FH=17$, and $GH=21$, find the perimeter of $\triangle IJ

1. **Problem Statement:** We are given triangle $\triangle TUV$ with points $E$, $D$, and $H$ as midpoints of its sides. The side lengths are $UV=40$, $TV=50$, and the segment $HD=

1. **State the problem:** We need to find the volume of a triangular prism. The volume is given by the formula: volume = area of the triangular base \( \times \) height of the pris

1. **State the problem:** We need to find the approximate volume of a cylindrical aluminum can with height $h = 8$ inches and radius $r = 1.5$ inches. 2. **Formula for volume of a

1. **State the problem:** We need to find the volume of a rectangular prism with height $35$ cm, width $39$ cm, and depth $27$ cm. 2. **Formula for volume of a rectangular prism:**

1. **State the problem:** We need to find the surface area of wrapping paper required to cover a present with dimensions 6 in. long, 5 in. wide, and 3.5 in. tall. 2. **Formula used

1. **State the problem:** We need to find the surface area of a hemisphere with radius $r=57$ meters, including the circular base. 2. **Formula used:** The surface area $A$ of a he

1. The problem asks for the exponent used to express the volume of a cube with edge length 21 cm. 2. The formula for the volume $V$ of a cube with edge length $a$ is:

1. **Problem statement:** We are given a triangle QRP with points R, S, and P on a straight line (RSP). The angle \(\angle QSP = 80^\circ\) and line QS is perpendicular to RS. We n

1. **Problem statement:** We have a 30-60-90 right triangle. The altitude to the hypotenuse is divided into two segments of lengths $x$ and $y$ by the median to the hypotenuse. We

1. **Problem Statement:** We have three polygons: an equilateral triangle, a rhombus with a 60° angle, and a regular hexagon. Each contains mutually tangent congruent disks. We den