Help me find the area

Question

A children’s play area is triangular. The sides of the play area measure 100m, 250m and 275m respectively. Calculate the area of the play area.

Answer 1

Sketching out the triangle, we can add a "height" which we will need to calculate area, and an angle (∠A) which we can use to calculate the height.

To find ∠A, we can use the Law of Cosines.

100² = 250² + 275² - 2(250)(275)cos(A)

10,000 = 62,500 + 75,625 - 137,500cos(A)

-128,125 = -137,500cos(A)

cos(A) = 0.931818

A = cos^-1(0.931818) = 21.279966°

Now, we can calculate h using sine. sin(21.279966°) = h/250 or h = 250sin(21.279966°) = 90.73136.

Now, the area = 1/2bh = 1/2(275)(90.73136) = 12,475.6 sq m