Find the area of the quadrilateral.
the numbers are 9, 4, 6, and 5.
Responses:
A. 60 cm2
B. 30 cm2
C. 24 cm2
D. 54 cm2
To find the area of a quadrilateral, you can split it into two triangles and then find the area of each triangle.
Using the numbers provided, let's split the quadrilateral into two triangles with sides 9, 4, and 6 (triangle 1) and sides 6, 5, and 4 (triangle 2).
For triangle 1, using Heron's formula:
s = (9 + 4 + 6) / 2 = 19 / 2 = 9.5
Area = √(9.5 * (9.5 - 9)(9.5 - 4)(9.5 - 6)) = √(9.5 * 0.5 * 5.5 * 3.5) = √(95.625) ≈ 9.78 cm2
For triangle 2, using Heron's formula:
s = (6 + 5 + 4) / 2 = 15 / 2 = 7.5
Area = √(7.5 * (7.5 - 6)(7.5 - 5)(7.5 - 4)) = √(7.5 * 1.5 * 2.5 * 3.5) = √(87.1875) ≈ 9.34 cm2
Therefore, the total area of the quadrilateral is the sum of the areas of the two triangles:
9.78 + 9.34 = 19.12 cm2
So the closest option would be C. 24 cm2, but the actual area is 19.12 cm2.