Geometry

The perimeter \(P\) of a rectangle is given by \(P = 2 \times (\text{length} + \text{width})\).

So, \(P = 2 \times (10\,\text{cm} + 5\,\text{cm}) = 30\,\text{cm}\).

The area \(A\) of a square is given by \(A = \text{side}^2\).

So, \(A = 6^2 = 36\,\text{cm}^2\).

The circumference \(C\) of a circle is given by \(C = 2\pi r\).

So, \(C = 2 \times \pi \times 4 = 8\pi\,\text{cm}\).

The volume \(V\) of a cube is given by \(V = \text{side}^3\).

So, \(V = 3^3 = 27\,\text{cm}^3\).

The perimeter \(P\) of a triangle is the sum of its sides.

So, \(P = 3 + 4 + 5 = 12\,\text{cm}\).

The area \(A\) of a triangle is given by \(A = \frac{1}{2} \times \text{base} \times \text{height}\).

So, \(A = \frac{1}{2} \times 8 \times 5 = 20\,\text{cm}^2\).

The circumference \(C\) of a circle is given by \(C = \pi d\).

So, \(C = \pi \times 10 = 10\pi\,\text{cm}\).

The volume \(V\) of a rectangular prism is given by \(V = \text{length} \times \text{width} \times \text{height}\).

So, \(V = 4 \times 3 \times 2 = 24\,\text{cm}^3\).

The area \(A\) of a rectangle is given by \(A = \text{length} \times \text{width}\).

So, \(A = 7 \times 4 = 28\,\text{cm}^2\).

The perimeter \(P\) of a square is given by \(P = 4 \times \text{side}\).

So, \(P = 4 \times 5 = 20\,\text{cm}\).

The volume \(V\) of a cylinder is given by \(V = \pi r^2 h\).

So, \(V = \pi \times 3^2 \times 5 = 45\pi\,\text{cm}^3\).

The area \(A\) of a circle is given by \(A = \pi r^2\).

So, \(A = \pi \times 7^2 = 49\pi\,\text{cm}^2\).

The area \(A\) of a parallelogram is given by \(A = \text{base} \times \text{height}\).

So, \(A = 10 \times 6 = 60\,\text{cm}^2\).

The perimeter \(P\) of an equilateral triangle is given by \(P = 3 \times \text{side}\).

So, \(P = 3 \times 9 = 27\,\text{cm}\).

The volume \(V\) of a cone is given by \(V = \frac{1}{3} \pi r^2 h\).

So, \(V = \frac{1}{3} \times \pi \times 3^2 \times 4 = 12\pi\,\text{cm}^3\).

The perimeter \(P\) of a pentagon is given by \(P = 5 \times \text{side}\).

So, \(P = 5 \times 6 = 30\,\text{cm}\).

The volume \(V\) of a rectangular prism is given by \(V = \text{length} \times \text{width} \times \text{height}\).

So, \(V = 5 \times 4 \times 3 = 60\,\text{cm}^3\).

The sum of the interior angles of any triangle is always \(180\) degrees.

In a right triangle, the sum of all angles is \(180\) degrees.

Since one angle is \(90\) degrees, the sum of the other two angles is \(180 - 90 = 90\) degrees.

A square has all sides of equal length and all angles of equal measure (each angle is \(90\) degrees).

The distance from the center to any point on the circle is called the radius.

A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides.

A cube has \(6\) faces.

A triangle with sides of \(3\) cm, \(4\) cm, and \(5\) cm is a right triangle because it satisfies the Pythagorean theorem: \(3^2 + 4^2 = 5^2\).