Grade 7: Geometry and Measurement
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Questions and Answers

What is the formula to find the area of a triangle?

  • A = base * height / 2 (correct)
  • A = base * height
  • A = base / height * 2
  • A = base + height

    • What is the circumference of a circle with a radius of 7 cm?

  • 21π cm
  • 35π cm
  • 28π cm
  • 14π cm (correct)

    • If a trapezoid has a height of 5 cm and bases of 8 cm and 12 cm, what is its area?

  • 50 cm²
  • 70 cm²
  • 65 cm² (correct)
  • 60 cm²

    • What is the perimeter of a triangle with sides of 5 cm, 6 cm, and 7 cm?

    <p>18 cm</p> Signup and view all the answers

    What is the area of a circle with a diameter of 14 cm?

    <p>63π cm²</p> Signup and view all the answers

    What is the approximate value of π?

    <p>3.14</p> Signup and view all the answers

    The area of a parallelogram is equal to its base multiplied by its height.

    <p>True</p> Signup and view all the answers

    What is the key concept to remember when calculating the area of a triangle?

    <p>The base and height must be perpendicular to each other.</p> Signup and view all the answers

    The circumference of a circle is equal to __________ times π times the diameter.

    <p>2</p> Signup and view all the answers

    Match each shape with its corresponding formula:

    <p>Circle = C = πd Parallelogram = A = bh Triangle = A = (bh)/2</p> Signup and view all the answers

    Opposite angles in a parallelogram are always unequal.

    <p>False</p> Signup and view all the answers

    Study Notes

    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

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    Test your knowledge and understanding of geometry and measurement concepts, including area and perimeter of circles, triangles, trapezoids, and parallelograms. Apply your skills to real-world problems!

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