Rhombus and trapezoid area

1. Area of rhombus
In the rhombus of the picture, the greater diagonal is AC and the less diagonal is BD. If we draw in the four vertices the parallels to the diagonals, we obtain a rectangle whose side is the less diagonal BD and whose height is the greater diagonal AC. If we call the diagonals d and D, the area of the rectangle will be d x D, which has 8 triangles. As the rhombus has the four interior triangles, its area will be the half of the rectangle: D x d/2.
The area of a rhombus is equal to half a product of lengths of two diagonals.

 Find the area of a rhombus whose diagonals are 3 dam and 8 m. A rhombus is D = 7 hm and d = 12 dam. How many m2 is it? Find the area of a rhombus whose diagonals are 3. 5 dam and 0.12 hm

2. Area of trapezium
If we cut the red trapezoid and we put it reversed next to the blue trapezoid, we obtain a parallelogram formed by two equal trapezoids.
The width of the parallelogram is b + b ' and the height is h. Its area is (b + b') x h.
The area of the trapezoid is one-half the height times the sum of the bases, that is, (b + b') x h/2.

 Find the area of a trapezium whose bases are 6 cm and 4 cm and its height is 2 cm. The bases of a trapezium are 8 dm and 6 dm and its height is 32 cm. What is its area? Find the area of a trapezium whose height is 0.6 m and the bases are 15 dm and 1.2m.

3. Exercises

 What is the area of the trapezium 1? What is the area of the rectangle 2? What is the perimeter of the rectangle 2? Find the area of the rhomboid 3. Find the area of the triangle 4.

4. Problems