Find the area of the triangle. Use the formula sheet provided.
Numbers given: 7cm 11cm 5cm 13cm
To find the area of the triangle, we will use the formula:
Area = 1/4 √(4a^2b^2 - (a^2 + b^2 - c^2)^2)
where a, b, and c are the lengths of the triangle's sides.
Given sides: a = 7cm, b = 11cm, c = 13cm, and a = 5cm
We will substitute these values into the formula:
Area = 1/4 √(4(7^2)(11^2) - (7^2 + 11^2 - 13^2)^2)
Area = 1/4 √(4(49)(121) - (49 + 121 - 169)^2)
Area = 1/4 √(24316 - (121)^2)
Area = 1/4 √(24316 - 14641)
Area = 1/4 √(9675)
Area = 1/4 * 98.36
Area = 24.59 cm^2
Therefore, the area of the triangle is 24.59 square centimeters.
Do it again without 5cm
Given sides: a = 7cm, b = 11cm, c = 13cm
We will use Heron's formula to find the area of the triangle:
First, calculate the semiperimeter (s):
s = (a + b + c) / 2
s = (7 + 11 + 13) / 2
s = 31 / 2
s = 15.5
Now, calculate the area using Heron's formula:
Area = √(s(s - a)(s - b)(s - c))
Area = √(15.5(15.5 - 7)(15.5 - 11)(15.5 - 13))
Area = √(15.5 * 8.5 * 4.5 * 2.5)
Area = √(1176.875)
Area ≈ 34.31 cm^2
Therefore, the area of the triangle is approximately 34.31 square centimeters.
(1 point)
Responses
32.5 cm2
32.5 cm2
45.5 cm2
45.5 cm2
65 cm2
65 cm2
71.5 cm2
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