Question

In rhombus ABCD, AB=14 and AC=19. Find the area of the rhombus to the nearest tenth. A 190.7 B 228.3 C 195.4 D 179.8

Answer 1

Answer:

C

Step-by-step explanation:

The triangle ABC has two sides that are 14 and 1 side that is 19. We can use Heron's formula to Calculate ABC.

s = (a + b + c)/2

s = (14 + 14 + 19)/2 = 23.5

s - a = 23.5 - 14 = 9.5

s - b = 23.5 - 14 = 9.5

s - c = 23.5 - 19 = 4.5

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Area = sqrt(s * (s - a) * (s - b) * (s - c) )

Area = sqrt(23.5 * 9.5 * 9.5 * 4.5)

Area = sqrt(9543,9)

Area = 97.69

But ABC is only 1/2 the rhombus. The area is twice that amount.

Area = 2 * 97.69 = 195.4