Geometery - 2D Shapes Flashcards
What is the formula for the area and perimeter of a rectangle?
Area = Length x Width
Perimeter = 2 x (Length x Width)
What is the formula for the area and perimeter of a triangle?
Area = (Base x Height) ÷ 2
Perimeter = Side 1 + Side 2 + Side 3
What is the formula for the circumference and area of a circle?
Area = π x radius^2
Circumference = π x diameter
What is the formula for the area and perimeter of a trapezium?
Area = ((top + bottom) x height) ÷ 2
Perimeter = (All the sides added together)
What is the formula for the area and perimeter of a sector of a circle?
Area = (Center Angle ÷ 360) x (π x radius)
Perimeter = (2 x radius) + (diameter x π) ÷ (Center Angle ÷ 360)
Find the radius of a circle if a 20* arc on the circle has a length of 4π.
4π = 20 ÷ 360 x 2πr
36 = r
Answer: Radius = 36cm
A trapezium has parallel sides of lengths 10 cm and 6 cm, and the height is 4 cm. What is the area of the trapezium?
A circle has a radius of 5 cm. What is the circumference of the circle? What is the area of the circle? (Use 𝜋 =3.14)
A right-angled triangle has a base of 8 cm and a height of 6 cm. What is the area of the triangle? Find the length of the hypotenuse.
A parallelogram has a base of 15 cm and a height of 8 cm. What is the area of the parallelogram? If the length of one side of the parallelogram is 13 cm, what is the perimeter?
A shape consists of a rectangle and a semicircle. The rectangle has a length of 12 cm and a width of 6 cm. The semicircle has a diameter equal to the width of the rectangle. What is the total area of the compound shape? (Use 𝜋 =3.14)
Rectangle: 12 x 6 = 72cm^2
Semicircle: (𝜋 x 3^2) ÷ 2 = 14.13 cm^2
72 + 14.13 = 86.13cm^2
The total area of this shape is 86.13cm^2.
A triangle has interior angles x°, (2x - 10)°, and (3x + 20)°. Find the value of x and the three angles of the triangle. Round to 2 decimal points.
Add all the co-efficients:
x + 2x + 3x = 6x°
-10 + 20 = 10°
Sum of interior angles in a triangle:
6x° + 10° = 180°
6x° = 170°
x = 28.33°
(2x - 10) = 46.67°
(3x + 20) = 105°
A quadrilateral has interior angles 90°, (2y + 10)°, (y + 30)°, and (3y - 20)°. Find the value of y and the unknown 3 angles of the quadrilateral. Round to 2 decimal points.
Add all the co-efficients:
2y + y + 3y = 6y°
90 + 10 + 30 - 20 = 110°
Sum of interior angles in a quadrilateral:
6y° + 110° = 360°
6y° = 250°
y = 41.67°
(2y + 10) = 93.33°
(y + 30) = 71.67°
(3y - 20) = 105°
A regular polygon has 10 sides.
1) Find the sum of the interior angles of the polygon.
2) Find the size of one interior angle.
3) Find the size of one exterior angle.
(10 - 2) x 180° = 1440°
1) 1440°
1440° ÷ 10 = 144°
2) 144°
360° ÷ 10 = 36°
3) 36°
Three angles on a straight line are (2x + 10)°, (3x - 5)°, and (x + 15)°. Find the value of x and the three angles.
Add all the co-efficients:
2x + 3x + x = 6x°
10 - 5 + 15 = 20°
Sum of angles on a straight line:
6x° + 20° = 180°
6x° = 160°
x = 26.67°
(2x + 10) = 63.33°
(3x - 5) = 75°
(x + 15) = 41.67°
