Grade 7: Geometry and Measurement

Geometry Essentials

• Geometry is the branch of mathematics that deals with the study of shapes, sizes, and positions of objects.

Area of Circle

• The area of a circle is found using the formula: A = πr^2, where A is the area and r is the radius of the circle.
• π (pi) is a mathematical constant approximately equal to 3.14.
• The area of a circle is always in square units.

Circumference of Circle

• The circumference of a circle is the distance around the circle.
• The formula to find the circumference of a circle is: C = 2πr, where C is the circumference and r is the radius.

Area of Trapezoid

• A trapezoid is a quadrilateral with two pairs of opposite sides, where one pair is parallel.
• The formula to find the area of a trapezoid is: A = (1/2)h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the parallel sides.

Area of Triangle

• The formula to find the area of a triangle is: A = (1/2)bh, where A is the area, b is the base, and h is the height.

Perimeter of Triangle

• The perimeter of a triangle is the distance around the triangle.
• The formula to find the perimeter of a triangle is: P = a + b + c, where P is the perimeter, and a, b, and c are the lengths of the sides.

Perimeter of Parallelogram

• A parallelogram is a quadrilateral with opposite sides that are parallel.
• The formula to find the perimeter of a parallelogram is: P = 2(a + b), where P is the perimeter, and a and b are the lengths of the sides.

Circumference of Circles

• Circumference is the distance around a circle
• Formula: C = 2 × π × radius (r) or C = π × diameter (d)
• π (pi) is approximately 3.14, a constant ratio of circumference to diameter
• Measuring circumference has real-world applications, such as measuring a circular garden bed or a circular pipe

Area of Parallelograms

• Area is calculated by multiplying base (b) and height (h): A = b × h
• Base and height are perpendicular to each other
• Opposite sides of a parallelogram are equal in length
• Opposite angles of a parallelogram are equal
• Diagonals of a parallelogram bisect each other
• Measuring area has real-world applications, such as measuring a rectangular backyard or a rectangular room

Area of Triangles

• Area is calculated by multiplying base (b) and height (h) and dividing by 2: A = (b × h) / 2
• Base and height are perpendicular to each other
• Sum of interior angles of a triangle is 180°
• Exterior angles of a triangle are equal to the sum of the two non-adjacent interior angles
• Measuring area has real-world applications, such as measuring a triangular garden bed or a triangular roof