📐 geometry

1. **Problem Statement:** Calculate the areas of:

1. **Problem Statement:** Calculate the area of:

1. **State the problem:** We are given a tank with dimensions length $L=50$ cm, width $W=110$ cm, and height $H=30$ cm.

1. **State the problem:** We are given a rectangular tank and need to verify the total surface area (T.S.A) calculation, calculate the volume, and find the height of water when 40

1. **Stating the problem:** We want to understand why $\angle EHF = \angle BED$ due to alternate interior angles, and why $\angle EHF \neq \angle BEH$. 2. **Key concept:** Alternat

1. **State the problem:** Given that $HF \parallel BE$, $\angle HEF$ and $\angle BDC$ are complementary, and $\angle BDE$ and $\angle BDC$ are complementary, prove that $$\frac{HF}

1. **Problem Statement:** Find the secant of angle $V$ in the right triangle $UVW$ where $\angle U$ is the right angle, $UW=48$, $UV=20$, and hypotenuse $VW=52$. 2. **Recall the de

1. **State the problem:** Calculate the cross-sectional area and volume of a cylinder with radius $r=15$ cm and height $h=17$ cm.

1. **State the problem:** Calculate the volume of a cylinder with radius $r=15$ cm and height $h=27$ cm. 2. **Formula:** The volume $V$ of a cylinder is given by the formula:

1. **State the problem:** We have a right-angled triangle with hypotenuse 8.6 cm, base 6.9 cm, and height $x$ cm. We need to find $x$ correct to 3 significant figures. 2. **Formula

1. **State the problem:** We have a right triangle with legs measuring 5.4 cm and 12.8 cm, and we need to find the length of the hypotenuse $x$ cm. 2. **Formula used:** In a right

1. **State the problem:** Solve for $x$ given the segments on parallel lines cut by transversals with lengths $7x - 11$, $4x - 2$, $20$, and $35$. 2. **Use the Segment Proportional

1. **Problem statement:** Given a circle with center O and points C, B, A, D on the circumference, the measure of angle CDB is 57°. We need to find the measure of angle CDA. 2. **R

1. **State the problem:** We have a circle with center $O$ and points $P$, $Q$, and $R$ on the circumference. The arc $PQR$ has length 14 and radius $r$.

1. **State the problem:** We have a circle with center O and two radii forming an angle of 42° at the center. We need to find the value of the angle $x$ at the circumference subten

1. **Find the volume of the triangular prism.** The formula for the volume of a prism is:

1. The problem appears to involve a set of lengths: 2 cm, 7 cm, 4 cm, 5 cm, and 2 cm. 2. Since no specific question is given, let's assume we want to find the perimeter of a polygo

1. **State the problem:** We need to find the angle $x^\circ$ in a right triangle with sides adjacent to the right angle measuring 6 units and 3.3 units. 2. **Identify the sides re

1. **State the problem:** We have a right triangle IHG with a right angle at H. Given: IH = 9.5, GH = 4.1, and we need to find angle $x$ at vertex G.

1. **State the problem:** We have two similar right triangles \(\triangle ABC \sim \triangle YXZ\) with a right angle at \(C\) in \(\triangle ABC\) and at \(Z\) in \(\triangle YXZ\

1. 문제: 사다리꼴의 넓이를 구하시오. 2. 사다리꼴 넓이 공식은 $$\text{넓이} = \frac{(\text{윗변} + \text{밑변}) \times \text{높이}}{2}$$ 입니다.