Find the area of the triangles in square centimeters:
a. 3.5, 4.8, 6.1
b. 10.2, 4.4, 7.1
I will do the 1st one
you do the 2nd
method 1. check to see if it is right -angled, then it would be real easy
is 3.5^ + 4.8^2 = 6.1^2 ? , NO
--- so forget that method
method 2:
find the angle opposite the smallest side using the cosine law
3.5^2 = 4.8^2 + 6.1^2 - 2(4.8)(6.1)cosØ
cosØ = .819672..
Ø = 34.948°
then area = (1/2)(4.8)(6.1)sin 34.948°
= appr. 8.386
Method 3.
Heron's Formula
(If a, b, and c are the three sides and s = (1/2) perimeter, then
Area = √( s(s-a)(s-b)(s-c) )
s = (1/2) (3.5+4.8+6.1) = 7.2
s-a = 3.7
s-b = 2.4
s-c = 1.1
A = √(7.2x3.7x2.4x1.1) = appr 8.386
same as method 2 answer
Use Heron's formula.
Let a, b and c be the sides of a triangle.
Let s = a + b + c
Therefore the area of triangle can be calculated using this formula:
A = sqrt[ (s)(s-a)(s-b)(s-c) ]
It should be a little easy using this formula, so I guess you can do it on your own. :)
Hope this helps :3
To find the area of a triangle, we need the length of the base and the height. The formula to calculate the area of a triangle is:
Area = (base * height) / 2
a. Before we can calculate the area, we need to identify the base and height of the triangle. Since the lengths of the sides are given (3.5, 4.8, and 6.1), we cannot directly determine the base and height. However, we can use the Heron's formula to find the area.
Heron's formula states that the area of a triangle with sides a, b, and c can be calculated using the semi-perimeter (s) of the triangle:
s = (a + b + c) / 2
Once we have the semi-perimeter, we can calculate the area using the formula:
Area = √(s * (s - a) * (s - b) * (s - c))
Let's apply this to the given triangle:
a = 3.5, b = 4.8, c = 6.1
s = (a + b + c) / 2
s = (3.5 + 4.8 + 6.1) / 2
s = 14.4 / 2
s = 7.2
Area = √(7.2 * (7.2 - 3.5) * (7.2 - 4.8) * (7.2 - 6.1))
Area ≈ √(7.2 * 3.7 * 2.4 * 1.1)
Area ≈ 5.262 square centimeters
Therefore, the area of the triangle with side lengths 3.5, 4.8, and 6.1 is approximately 5.262 square centimeters.
b. Let's apply the same approach to the second triangle with side lengths 10.2, 4.4, and 7.1:
a = 10.2, b = 4.4, c = 7.1
s = (a + b + c) / 2
s = (10.2 + 4.4 + 7.1) / 2
s = 21.7 / 2
s = 10.85
Area = √(10.85 * (10.85 - 10.2) * (10.85 - 4.4) * (10.85 - 7.1))
Area ≈ √(10.85 * 0.65 * 6.45 * 3.75)
Area ≈ 16.289 square centimeters
Therefore, the area of the triangle with side lengths 10.2, 4.4, and 7.1 is approximately 16.289 square centimeters.