📐 geometry

1. **State the problem:** We are given two triangles ABC and ECD with AB parallel to ED, and lines ACD and BCE are straight. We know the lengths AB = 8 cm, AC = 4.8 cm, BC = 6.4 cm

1. **Problem statement:** A cone is divided into a small cone and a frustum. The curved surface area of the small cone is $15\pi$ cm², the curved surface area of the frustum is $12

1. **State the problem:** We have a circle with equation $$(x - 5)^2 + y^2 = 25$$ and a point $$P(8,4)$$ on the circle. We need to find the y-coordinate of point $$Q$$ where the ta

1. **Problem Statement:** We have a quadrant ABC which is a quarter circle with center A and radius AB = 12 cm.

1. **Problem Statement:** Two chords AB and CD intersect at right angles at point P inside a circle. Given lengths are AP = 4, PB = 12, CP = 8, and PD = 6 units. We need to find th

1. **Problem Statement:** Mahati draws a kolam pattern on a 3x3 grid of dots spaced 1 unit apart horizontally and vertically. The continuous line encloses all dots, crossing itself

1. **Problem Statement:** We are given four side lengths: 5, 9, 12, and 13, and asked to solve the triangle. However, a triangle can only have three sides. We need to clarify which

1. **Problem Statement:** We have a right triangle with angles 30°, 60°, and 90°. The hypotenuse is 9 meters, the side opposite the 30° angle is 9 meters, and the side adjacent to

1. **State the problem:** Find the coordinates of a point on the y-axis that is equidistant from the points $(4,-2)$ and $(4,6)$. 2. **Recall the formula:** The distance between tw

1. **Problem statement:** We are given a circle centered at $(0,0)$ with an area of $9\pi$. We need to determine which point the circle does not pass through. 2. **Formula for the

1. **State the problem:** We need to find the surface area of a rectangular prism with dimensions 5 units by 5 units by 8 units, where two faces have curved edges forming semicircl

1. The problem is to find the volume or surface area of a quarter cylinder, which is one-fourth of a full cylinder. 2. Recall the formulas for a full cylinder:

1. **Problem Statement:** Find the surface area of a semicylindrical solid with radius $r=5$ cm and length $l=8$ cm.

1. **Stating the problem:** We have a cuboid with volume 360 cm³ and surface area A cm².

1. **Stating the problem:** We want to find the area $A$ of a triangle given its base $b$ and height $L$. 2. **Formula used:** The area of a triangle is calculated by the formula:

1. **Problem Statement:** Reflect the polygon ABCD with vertices A(2, -2), B(-2, 2), C(0, 4), and D(4, 0) across the line $y = x$. 2. **Reflection Formula:** When reflecting a poin

1. **Problem Statement:** We have a benchmark blob with area $b$ cm$^2$. We need to estimate the areas of four different shapes in terms of $b$. 2. **Understanding the Problem:** T

1. **Problem statement:** We have a right-angled triangle ABC with right angle at B. AB is parallel to ED. The areas of triangles EDC and BED are 24 cm² and 72 cm² respectively. We

1. **Problem Statement:** In triangle $\triangle DEF$, point $C$ is the centroid. Given that $HD = 30x - 6y$, find the expression for $CD$.

1. **Problem Statement:** Identify a median in triangle $\triangle GBI$ using the given figure. 2. **Definition of a Median:** A median of a triangle is a line segment joining a ve

1. **Problem Statement:** We are given triangle $PQR$ with altitudes $\overline{RS}$ and $\overline{PT}$ drawn from vertices $R$ and $P$ respectively. The measure of angle $Q$ is $