Question

Please Help!

Answer 1

Using the Herons formula, calculate the area of the parallelogram to the nearest tenth of a square unit.

Area = 36.7 square units.

Answer 2

Diagonal of the parallelogram divides the parallelogram in to two equal areas.

So area of parallelogram = 2(area of triangle)

According to the given diagram,

AB= 8, AD = 5 and BD = 11

So according to the Heron's formula,

Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}\\\\where,\\ s =\frac{a + b + c }{2}$

and a, b and c are the three sides of the triangle

Area of triangle ABD =$s=\frac{8 + 5 + 11}{2} \\\\s = \frac{24}{2}\\\\s = 12Area of triangle ABD = \sqrt{12(12 - 8) (12 - 5) (12 - 11)}\\\\Area of triangle ABD = \sqrt{12(4) (7) (1)}\\\\Area of triangle ABD = \sqrt{336}\\\\Area of triangle ABD = 18.33$

So, area of parallelogram ABCD = 2(area of triangle ABD)

area of parallelogram ABCD = 2 (18.33)

area of parallelogram ABCD = 36.66

area of parallelogram ABCD = 36.7 sq. units