B. 240 cm2
To find the area of the quadrilateral, we can divide it into two triangles and calculate their individual areas.
Let's label the sides of the quadrilateral as a, b, c, and d, with a = 10, b = 24, and c = 20.
We can calculate the semi-perimeter of the quadrilateral using the formula:
s = (a + b + c + d) / 2
s = (10 + 24 + 20) / 2
s = 54 / 2
s = 27
Now, we can calculate the area of each triangle using Heron's formula. Let's take triangle ABC (with sides a, b, and c):
Area(ABC) = sqrt[s * (s-a) * (s-b) * (s-c)]
Area(ABC) = sqrt[27 * (27-10) * (27-24) * (27-20)]
Area(ABC) = sqrt[27 * 17 * 3 * 7]
Area(ABC) = sqrt[27 * 357]
Area(ABC) = sqrt(9615)
Area(ABC) ≈ 98.06 cm2
Similarly, we can calculate the second triangle's area (ACD) in the same manner:
Area(ACD) = sqrt[s * (s-a) * (s-c) * (s-d)]
Area(ACD) = sqrt[27 * (27-10) * (27-20) * (27-24)]
Area(ACD) = sqrt[27 * 17 * 7 * 3]
Area(ACD) = sqrt[27 * 357]
Area(ACD) = sqrt(9615)
Area(ACD) ≈ 98.06 cm2
Therefore, the total area of the quadrilateral is the sum of the two triangle's areas:
Total Area = Area(ABC) + Area(ACD)
Total Area ≈ 98.06 + 98.06
Total Area ≈ 196.12 cm2
So, the total area of the quadrilateral is approximately 196.12 cm2, which is closest to option B. 240 cm2.
What is the area of the quadrilateral?
the numbers are 10, 24, and 20.
Responses:
A. 480 cm2
B. 240 cm2
C. 460 cm2
D. 220 cm2
1 answer