1. A parallelogram with opposite equal acute and obtuse angles and four equal sides. Diagonals 4 equal sides

2. Same as Area of parallelogram A = b. h b h

3. Since the diagonals are perpendicular Another way to find the area of a rhombus is: Area = ½ (product of the diagonals) d1d1 d2d2 area = ½ (d 1. d 2 ) This is good when you only know the diagonals, but not the sides or height

4. The diagonals divide a rhombus into 4 congruent right triangles. So, the area of the rhombus is 4 times the area of one of the right triangles. Area of 1 triangle = 1/2bh = ½( 3 )(4) = 6 Area of 4 triangles = 4(6) = 24 Notice that 1/2d 1 d 2 or ½(6)(8), also equals 24 The formula for the area of a rhombus can be justified using the area of a triangle. A specific case follows.

5. Find the Area of a Rhombus Example 3 Find the area of the rhombus. a.b. = 108 The area of the rhombus is 70 square inches. The area of the rhombus is 108 square inches. SOLUTION A = d 1 d 2 2 1 a. SOLUTION b. A = d 1 d 2 2 1 2 1 (14)(10)= (6 + 6)(9 + 9)= 2 1 = 70 (12)(18)= 2 1