# How to find the area of a trapeze if the bases are known

By geometrical definition a trapeze is the quadrangle at which only one couple of the parties is parallel. These parties are its bases. The distance between the bases is called trapeze height. It is possible to find the area of a trapeze, using geometrical formulas.

## Instruction

1. Measure the bases and height of a trapeze of AVSD. Usually their size is given in statements of the problem. Let the basis of AD (a) of a trapeze will be equal in this example of the solution of a task 10 cm, the basis of BC (b) - 6 cm, height of a trapeze of BK (h) - 8 cm. Apply a geometrical formula to finding of the area of a trapeze if lengths of its bases and height - S = are known 1/2 (a+b) of *h where: - a - ABCD trapeze AD basis size, - b - BC basis size, - h - BK height size.

2. Find the sum of lengths of the bases of a trapeze: AD + BC (10 cm + 6 cm = 16 cm). Divide the received sum into 2 (16/2=8 cm). Increase the received number by ABCD trapeze VS height length (8*8 = 64). So, the area of a trapeze of ABCD with the bases, equal 10 both 6 cm, and height equal of 8 cm, will be equal 64 quarter see.

3. Measure the bases and sides of a trapeze of AVSD. Let the basis of AD (a) of a trapeze will be equal in this example of the solution of a task to 10 cm, the basis of BC (b) - 6 cm, the party of AB (c) - 9 cm and side of CD (d) - 8 cm. Apply a formula to finding of the area of a trapeze if its bases and sides - S=(a+b)/2 * (√ s2 - ((b-a)2+c2-d2 / (2 (b-a)) 2 where are known: - a - ABCD trapeze AD basis size, - b - BC basis size, - with - AB side size, - d - CD side size.

4. Substitute lengths of the bases of a trapeze a formula: S=(a+b)/2 * (√ s2 - ((b-a)2+c2-d2 / (2 (b-a)) 2. Solve the following expression: (10+6)/2 * √ (9*9-((10-6)2+(9*9-8*8) / (2*(10-6))2. For this purpose simplify expression, having made calculations in brackets: 8 * √ 81-((16+81-64)/8)2 = 8 * √ (81-17). Find value of the work: 8 * √ (81-17)=8*8=64. So, the area of a trapeze of ABCD with the bases, equal 10 both 6 cm, and sides, equal 8 and 9 cm will be equal 64 quarter see.

Author: «MirrorInfo» Dream Team