Question

Основания трапеции отличаются друг от друга на 6 см. Высота трапеции равна 8 см. Найди основания трапеции, если ее площадь равна 56 см2

Answer 1

Длины оснований обозначим а и b, высоту обозначим h. Тогда 56=h*0,5*(a+b)⇒56=8*0,5*(a+b)⇒a+b=14. Так как по условию a-b=6⇒a=b+6⇒2*b+6=14⇒b=4; а=6+4=10.

Ответ: 4 см и 10 см.

Answer 2

Given Information:

We are given that the bases of a trapezoid (trapezium) differ from each other by 6 cm and the height of the trapezoid is 8 cm. The area of the trapezoid is given as 56 cm².

Solution:

To find the bases of the trapezoid, we can use the formula for the area of a trapezoid:

Area = (1/2) * (sum of bases) * height

Let's denote the lengths of the bases as b1 and b2.

From the given information, we have the following equations:

1. b2 - b1 = 6 (the bases differ from each other by 6 cm) 2. (1/2) * (b1 + b2) * 8 = 56 (the area of the trapezoid is 56 cm²)

We can solve this system of equations to find the values of b1 and b2.

Solving the Equations:

Let's solve the system of equations using substitution or elimination method.

From equation 1, we can express b2 in terms of b1:

b2 = b1 + 6

Substituting this value of b2 in equation 2, we get:

(1/2) * (b1 + (b1 + 6)) * 8 = 56

Simplifying the equation:

(1/2) * (2b1 + 6) * 8 = 56

(b1 + 3) * 8 = 56

b1 + 3 = 7

b1 = 7 - 3

b1 = 4

Substituting this value of b1 in equation 1, we can find b2:

b2 = b1 + 6

b2 = 4 + 6

b2 = 10

Answer:

The bases of the trapezoid are 4 cm and 10 cm.

Please note that the solution provided is based on the given information and the assumption that the trapezoid is a right trapezoid (with one of the bases perpendicular to the height). If there are any additional constraints or information, please let me know.