Area of special quadrilaterals practice
1. Find the area of a trapezoid with bases of 8 and 12 and a height of 6.
Area = 1/2 * (base1 + base2) * height
Area = 1/2 * (8 + 12) * 6
Area = 1/2 * 20 * 6
Area = 10 * 6
Area = 60 square units
2. Find the area of a parallelogram with base of 10 and a height of 8.
Area = base * height
Area = 10 * 8
Area = 80 square units
3. Find the area of a rhombus with diagonals of 6 and 8.
Area = 1/2 * d1 * d2
Area = 1/2 * 6 * 8
Area = 24 square units
4. Find the area of a kite with diagonals of 10 and 12.
Area = 1/2 * d1 * d2
Area = 1/2 * 10 * 12
Area = 60 square units
5. Find the area of a rectangle with width of 7 and length of 9.
Area = width * length
Area = 7 * 9
Area = 63 square units
6. Find the area of a square with sides of 5.
Area = side^2
Area = 5^2
Area = 25 square units
7. Find the area of a cyclic quadrilateral with side lengths of 4, 6, 8, and 10.
To find the area of a cyclic quadrilateral, you can divide it into two triangles and use Heron's formula.
Area = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter and a, b, c are the side lengths.
Semi-perimeter (s) = (4 + 6 + 8 + 10) / 2 = 14
Area = sqrt(14 * (14 - 4) * (14 - 6) * (14 - 8) * (14 - 10))
Area = sqrt(14 * 10 * 8 * 6 * 4)
Area = sqrt(26880)
Area ≈ 163.93 square units
Practice calculating the areas of different types of quadrilaterals to strengthen your understanding of these geometric shapes and their properties.