11.8notes April 01, 2016

11.8 Hero's and Brahmagupta's Formula

Escher

11.8notes April 01, 2016

Hero's Formula (Theorem 111)

A = √s(s-a)(s-b)(s-c), where a,b,and c are the lengths of the sides of the triangle and s=semiperimeter =a+b+c.

2

a

c

b

11.8notes April 01, 2016

Find the area of a triangle with sides 4, 7, and 8.

11.8notes April 01, 2016

11.8notes April 01, 2016

Brahmagupta's Formula (Theorem 112)

A = √(s-a)(s-b)(s-c)(s-d), where a,b,c, and d are the sides of the quadrilateral and s=semiperimeter= (a+b+c+d)/2

cyclic quad

a

b

c

d

11.8notes April 01, 2016

Find the area of the inscribed quadrilateral with sides 2, 7, 6, and 9.

11.8notes April 01, 2016

11.8notes April 01, 2016

10

5 7

75

Find the area of the figure to the nearest hundredth.

11.8notes April 01, 2016

(-2,12)

(-2,3)

(15, 5)

Find the area of the triangle.

11.8notes April 01, 2016

55

68

5

Find the area of the pentagon to the nearest tenth.

11.8notes April 01, 2016

13

15

14Find the measures of the three altitudes of the triangle. (Hint: Use Hero's formula to find the area and then use the 1/2bh to find each altitude)

11.8notes April 01, 2016

Which has a greater area, a circle with a circumference of 100 or a square with a perimeter of 100?

11.8notes April 01, 2016