Find the area of the quadrilateral.

Question

the numbers are 9, 4, 6, and 5.
Responses:
A. 60 cm2
B. 30 cm2
C. 24 cm2
D. 54 cm2

Answer 1

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.