find the area of a polygon in square units 7,13,15,7

Answer 1

To find the area of a polygon, we need to know the shape of the polygon. If we assume that the polygon is a quadrilateral with side lengths of 7, 13, 15, and 7 units, we can calculate the area using the formula for the area of a quadrilateral when you know the lengths of all sides and the diagonals.

Let's first determine if the quadrilateral with sides 7, 13, 15, and 7 units is a valid polygon. To do this, we can use the triangle inequality theorem to check that the sum of the lengths of any two sides of a triangle should be greater than the length of the third side.

For our quadrilateral:
1. Side 1 + Side 2 > Side 3: 7 + 13 > 15 - True
2. Side 2 + Side 3 > Side 4: 13 + 15 > 7 - True
3. Side 3 + Side 4 > Side 1: 15 + 7 > 7 - True
4. Side 4 + Side 1 > Side 2: 7 + 7 > 13 - True

Since all inequalities hold true, the quadrilateral is a valid polygon.

Now we can calculate the area of the quadrilateral using this formula:

Area = √((s-a)(s-b)(s-c)(s-d) - abcdcos²(θ))/ 4

Where:
s = (a + b + c + d)/2
a = 7, b = 13, c = 15, d = 7 (side lengths)
θ = angle between a and b (if known)

Let's calculate the area:
s = (7 + 13 + 15 + 7)/2 = 21
Area = √((21-7)(21-13)(21-15)(21-7) - 7*13*15*7*(cos²(θ)))/4
Area = √(14*8*6*14 - 4095(cos²(θ)))/4
Area = √(18816 - 4095(cos²(θ)))/4

Without knowing the angle between sides a and b, we cannot determine the exact area. If you can provide the angle measure, we can calculate the area using the formula given above.