📐 geometry

1. **State the problem:** We need to find the perimeter of a figure composed of a parallelogram and a semicircle attached on the side of length 8. 2. **Identify the sides:** The pa

1. **State the problem:** We need to find the total volume of a solid made by joining a cylinder and a hemisphere, both having radius $1.5$ cm. The cylinder's height is $4$ cm. 2.

1. **Problem (d):** Show that a triangle with sides 10 cm, 5 cm, and 11 cm is not right-angled. 2. **Step 1:** Recall the Pythagorean theorem for right-angled triangles: $$a^2 + b^

1. **State the problem:** We need to find the perimeter of a figure composed of a rectangle and two semicircles attached to the vertical ends of the rectangle. 2. **Identify given

1. **State the problem:** We have an isosceles trapezoid with sides AB = 3x - 2, BC = 5x - 6, CD = 3x + 9, and AD = 4x + 5. We need to find the value of $x$ and then find $m\angle

1. **State the problem:** We have an isosceles triangle with two equal sides of 15 units each and a base of 7x units. The perimeter is given as 17x units. 2. **Write the formula fo

1. **State the problem:** We need to estimate the number of vertical cross sections required so that their total area equals the area of the base of a rectangular prism with dimens

1. **Problem statement:** Given triangles \(\triangle ACD\) and \(\triangle DFC\), find the length of \(FD\).\n\n2. **Given data:** \(CD = 12\), \(CF = 9\), \(DE = 9\), and \(EF\)

1. **Problem Statement:** Given an isosceles trapezoid front face of a sign with sides WX = $2x - 2$, YZ = $2x + 6$, WZ = $4x + 5$, and XY = $5x - 3$, prove $x=8$, find $m\angle Z$

1. **Stating the problem:** We are given a rectangular prism with dimensions 4 cm (height), 12 cm (length), and 3 cm (width). We need to find the length of the diagonal inside the

1. **State the problem:** We are given a circle with points P, Q, R, S on the circumference and angles 126°, 93°, and 90° at certain points. We need to find the measures of angles

1. **Problem statement:** Find the angle $\angle HFE$ in the given geometric figure. 2. **Identify known elements:** To find $\angle HFE$, we need information about points $H$, $F$

1. The problem asks: If you know the diameter of a circle, how can you find the area? 2. Recall the formula for the area of a circle: $$A = \pi r^2$$ where $r$ is the radius.

1. **State the problem:** Find the circumference of a circle with diameter 20 ft, using $\pi = 3.14$, and round to the nearest hundredth. 2. **Formula:** The circumference $C$ of a

1. **Stating the problem:** We need to find the measure of angle $HFE$ in the polygon with vertices $H, E, G, F$. Given are sides $HE=38$ cm, $EG=35$ cm, $GF=60$ cm, angles $\angle

1. Problem (a)(i): Construct the perpendicular bisector of chord [AB] using only a compass and straight edge. - To construct the perpendicular bisector of [AB], place the compass a

1. **Problem statement:** We have two intersecting lines AB and CD at point E.

1. **Problem statement:** We have two intersecting lines AB and CD at point E.

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

1. **State the problem:** We need to find the area of the yellow shape formed by two intersecting circles where the angle between the two radii is 100° and the distance between the

1. **State the problem:** We know that $\frac{3}{8}$ of the rectangle is shaded, and the shaded area is 72 m$^2$. The width of the rectangle is 12 m. We need to find the height of