📐 geometry

1. **State the problem:** We have a right triangle with legs of lengths 9 and 15, and we need to find the length of the hypotenuse. 2. **Formula used:** In a right triangle, the Py

1. Problem 9: Find the perimeter of triangle \(\triangle MNP\) with sides \(MN=22\), \(MP=25\), and \(NP=x+4\). Given angles \(\angle M=55^\circ\), \(\angle N=34^\circ\). 2. Use th

1. **State the problem:** We need to find the length $x$ of the side opposite the $55^\circ$ angle in a triangle where the other two sides are $19$ m and $17$ m. 2. **Formula used:

1. **Problem statement:** We have a cube with side length 7 cm and surface area 294 cm².

1. **Stating the problem:** We have an original cube with volume $V = 7 \times 7 \times 7 = 343$ cm$^3$.

1. **State the problem:** Calculate the area of a rectangle with width 23 yards and height 12 yards. 2. **Formula:** The area $A$ of a rectangle is given by the formula:

1. **State the problem:** Calculate the perimeter of a polygon with sides measuring 5 in., 3 in., 3 in., 5 in., 6 in., and 9 in. 2. **Formula:** The perimeter $P$ of a polygon is t

1. **Problem statement:** (a)(i) Given the circle $k$ with equation $$x^2 + y^2 = 49,$$ find the centre and radius.

1. **Problem statement:** We are given a children's slide with points X, Y, Z, U, V, and W.

1. **Problem statement:** In parallelogram ABCD, given that $ED = 7x - 13$ and $BD = 16x - 38$, find the length of diagonal $BD$. 2. **Key property:** In a parallelogram, the diago

1. **State the problem:** We are given two line segments \(\overline{DE}\) and \(\overline{FG}\) intersecting at point \(H\), where \(H\) is the midpoint of both segments. We know

1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°. The side opposite 30° is given as $22\sqrt{3}$, and we need to find the lengths of sides $x$ (hypo

1. **State the problem:** We need to find the area of a right triangle where one leg is 13 units and the angle adjacent to this leg is 51°. 2. **Identify the known values:**

1. **Problem statement:** Given triangles $\triangle ABC$ and $\triangle ADE$ are similar, find $x$. 2. **Known sides:**

1. **State the problem:** We need to find the volume of a composite solid consisting of a rectangular prism base and two triangular prisms on top. 2. **Identify the shapes and dime

1. **State the problem:** Alexis measured the distance across a dinner plate as 22 cm. We need to estimate the radius, diameter, and circumference of the plate.

1. **State the problem:** We need to estimate the area of a circle with a diameter of 40 feet using $\pi \approx 3.14$. 2. **Recall the formula for the area of a circle:**

1. **Stating the problem:** We need to find the value of $x$ given the angles and relationships in the diagram. 2. **Given information:**

1. **State the problem:** We are given three angles around a point: one is $90^\circ$, another is $40^\circ$, and the third is $(6x + 2)^\circ$. We need to find the value of $x$. 2

1. **Problem statement:** In trapezoid PQST, UR is the midsegment. Given bases PQ = 11 and TS = 18, find the length of UR. 2. **Formula for midsegment of trapezoid:** The midsegmen

1. **State the problem:** Plot the point $(-6, 1)$ on a Cartesian coordinate grid. 2. **Understanding the coordinate system:** The point $(-6, 1)$ means move 6 units to the left on