📐 geometry

1. **State the problem:** We need to find the surface area of a square-based pyramid with four identical triangular faces. The base side length is 30 mm, and each triangular face h

1. **State the problem:** We need to find the surface area of a square-based pyramid with a base side length of 9 cm and four identical triangular faces, each with a height of 14 c

1. **Stating the problem:** We are given two parallel horizontal lines intersected by two transversal lines, creating pairs of angles labeled a, b, c, d on the bottom intersection

1. **Problem statement:** We have a circle with points A, B, C, D on the circumference.

1. **Problem statement:** We have three parallel lines cut by a transversal, with angles labeled as in the diagram.

1. **State the problem:** Find the exact area swept by a windshield wiper of length $1.5$ m moving through an angle of $75^\circ$. 2. **Formula for area of a sector:** The area $A$

1. **State the problem:** We need to find the area swept by a windshield wiper of length $l=1.5$ m that moves through an angle of $75^\circ$. 2. **Formula for area of a sector:** T

1. **State the problem:** We have two similar trapezoidal shapes A and B. Shape A has sides: top = 4 cm, height = 12 cm, bottom = 7 cm.

1. **Stating the problem:** We have a quadrilateral with sides labeled as follows:

1. **Calculate the area of the rectangle with midpoints M(9,11) and N(5,8):** Given M and N are midpoints of two sides of the rectangle, and the sides are parallel to the axes.

1. **State the problem:** We need to find the coordinates of the center, $C$, of a rectangle given its bottom-left corner at $(4, -3)$ and top-right corner at $(18, 11)$. 2. **Form

1. **Problem:** Show that segments AB and CD are proportional given points dividing them and solve for unknowns in proportional segments. 2. **Proportional segments rule:** If two

1. **Stating the problem:** We need to find the volume of a cylindrical ring (a hollow cylinder) with outer diameter 30 cm, inner diameter 24 cm, and height 31 cm.

1. **State the problem:** Find the volume and surface area of a composite right prism made of two stacked rectangular prisms.

1. **State the problem:** We have a parallelogram DSOG with sides DO and OG labeled as expressions in terms of $p$: DO = $2p + 9$ and OG = $3p - 6$.

1. **State the problem:** We are given the cosine of angle A in a triangle with vertices A, B, and C, and the formula for cosine of angle A is given by the law of cosines: $$\cos A

1. **State the problem:** Find the circumference and area of a circle with radius $7$ cm, using $\pi = \frac{22}{7}$.\n\n2. **Formulas:**\n- Circumference $C = 2\pi r$\n- Area $A =

1. The problem asks: What is an angle whose vertex is on the circle and whose sides are chords of the circle? 2. Let's analyze the options:

1. The problem asks for the measure of angle $XYZ$ in the given figure. 2. The figure shows a circle with center $O$, points $X$ and $Z$ on the circle along a horizontal line throu

1. The problem is to plot the points A'(-2,3), B(1,-1), and C(3,-4) on a coordinate plane and understand the position of the number -8 in the bottom-right corner. 2. To plot points

1. **State the problem:** We have two circular arcs with the same center O and an angle of 120° each. The smaller arc has radius 1 cm, and the larger arc has radius 5 cm. We need t