7 in. 6in. 10in. 16in. what is the area of the quadrilateral?
To find the area of a quadrilateral, we need to split it up into two triangles and find the area of each triangle separately.
Given the sides of the quadrilateral are 7in, 6in, 10in, and 16in, we can first calculate the area of the triangle with sides 7in, 6in, and 10in using Heron's formula:
s = (a + b + c) / 2 = (7 + 6 + 10) / 2 = 11.5 in
Area of the triangle = √[s(s-a)(s-b)(s-c)] = √[11.5(11.5-7)(11.5-6)(11.5-10)] = √[11.5(4.5)(5.5)(1.5)] = √365.625 ≈ 19.12 in^2
Next, we calculate the area of the triangle with sides 10in, 16in, and the diagonal connecting the two triangles. The diagonal can be calculated using Pythagorean theorem:
diagonal^2 = 16^2 + 7^2 = 256 + 49 = 305
diagonal = √305 ≈ 17.46 in
Now, we can find the area of the second triangle using Heron's formula:
s = (a + b + c) / 2 = (10 + 16 + 17.46) / 2 ≈ 21.73 in
Area of the second triangle = √[s(s-a)(s-b)(s-c)] = √[21.73(21.73-10)(21.73-16)(21.73-17.46)] ≈ 44.07 in^2
Finally, the total area of the quadrilateral is the sum of the areas of the two triangles:
Total area = 19.12 + 44.07 ≈ 63.19 in^2
Therefore, the area of the quadrilateral is approximately 63.19 square inches.