📐 geometry

1. সমস্যা: একটি বৃত্ত যার কেন্দ্র O এবং ব্যাসার্ধ OA = 40 সেমি। কোণ OAC = 45° এবং OAB ও ABCA দ্বারা গঠিত আয়তন 320 বর্গ সেমি। এই তথ্য থেকে ABCA আয়তন নির্ণয় করতে হবে। 2. প্রথমে, O

1. **State the problem:** We have two similar triangles with sides 18 mm and 3 mm in the smaller triangle, and sides x mm and 10 mm in the larger triangle. We need to find the valu

1. **State the problem:** We have two similar trapezoids, Shape A and Shape B. We need to find:

1. **State the problem:** We have two similar shapes A and B. Shape A has height 8.5 cm and base width 3 cm. Shape B has base width 12 cm and unknown height $h$. We need to find $h

1. The problem states that shapes M and N are similar, meaning their corresponding sides are proportional. 2. For shape M, the sides are 4 m and $x$ m.

1. The problem asks to identify the mistake Beth made when calculating the curved surface area of the cone. 2. The formula for the curved surface area of a cone is $$\text{Curved s

1. **State the problem:** We have triangle ABC with sides AB = 3.2 cm, BC = 8.4 cm, and area = 10 cm². We need to find the perimeter of the triangle. 2. **Recall the formula for th

1. **State the problem:** We have triangle ABC with sides AB = 12 m, AC = 10 m, and BC = 15 m. We need to find the size of angle BAC (angle at vertex A). 2. **Identify sides relati

1. **Stating the problem:** We have a trapezoid ABCD with base AB as the diameter of a semicircle centered at point S. The trapezoid has height $v=6$ cm, the top side DC measures 4

1. Let's clarify the problem: we need to find angle $c$ in a triangle or geometric figure. 2. To find angle $c$, we need more information such as the other angles or sides of the t

1. **Stating the problem:** We have a parallelogram ABCD with sides |AB| = 5 cm, |BC| = 5.5 cm, and angle BAC = 45°. 2. **Understanding the figure:** In parallelogram ABCD, diagona

1. The problem asks for the formula of the area of a semicircle in terms of radians. 2. A semicircle is half of a full circle.

1. **State the problem:** We are given a triangle with vertices A, B, and C. Side AB = 10 cm, side AC = 8 cm, and angle B = 40°. 2. **Identify what is asked:** Find the size of ang

1. **State the problem:** We are given a triangle with angles $\angle EBH = 47^\circ$, $\angle ABE = 36^\circ$, and side length $BH = 7$ cm. We need to find the length of $AE$ to 2

1. **State the problem:** We are given a cuboid with angles $\angle EBH = 47^\circ$ and $\angle ABE = 36^\circ$, and length $BH = 7$ cm. We need to find the length $AE$ to 2 decima

1. **State the problem:** We have two similar cones. The smaller cone has volume $704$ mm³ and radius $8$ mm. The larger cone has volume $19,008$ mm³ and radius $r$. We need to fin

1. **State the problem:** We have a circle $C$ with equation $$x^2 + y^2 - 2x + 6y - 30 = 0.$$ Points $P(3,3)$ and $Q(7,-5)$ lie on $C$. We need to:

1. **State the problem:** We have two shapes, C and D, each with an area of $3^2 \times 13^2$ cm$^2$.

1. The problem asks to identify the types of angles marked in three different diagrams involving parallel lines and a transversal. 2. For (a), the two green angles are on opposite

1. Problem 22: Identify the terms related to a circle. - a. Tangent: A line that touches the circle at exactly one point.

**Problem 1:** Amy runs around a circular track. 1. a) Find the circumference if 8 laps equal 2000m.