The bases of the trapezium are 6 inches and 2 inches, the sides are 0.13 m and 0.37 m. Find the area of the trapezoid.

To solve the problem, you first need to draw a perpendicular height from the smaller base of the trapezoid to the larger one.

In this case, we get two right-angled triangles.

Since we know the lateral sides of the trapezoid, which are the hypotenuses of the triangle, we find the height by the Pythagorean theorem, where:

A – the first leg
B – the second leg (in this case, the height of the trapezoid)
C – hypotenuse (side of the trapezoid)
In this case, we get:

B ^ 2 = C ^ 2 – A ^ 2.

Since the trapezoid is not equilateral, we will compose a system of equations in which we write the height as x, and the first leg as y.

We translate the value of quantities into one dimension:

0.13 m = 1.3 dm.

0.37 m = 3.7 dm.

We find the difference in bases.

6 – 2 = 4 dm.

In this case, we get:

x ^ 2 + y ^ 2 = 1.3 ^ 2

x ^ 2 + (4 – y) ^ 2 = 3.7 ^ 2

Let us express x through the first equation:

x ^ 2 = 1.3 ^ 2 – y ^ 2.

Substitute the x value in the second equation:

1.3 ^ 2 – y ^ 2 + (4 – y) ^ 2 = 3.7 ^ 2.

(4 – y) ^ 2 – y ^ 2 = 3.7 ^ 2 – 1.3 ^ 2.

-8 * y = -4.

y = 4/8 = 0.5 dm.

Find the height x.

x ^ 2 + 0.5 ^ 2 = 1.3 ^ 2.

x ^ 2 + 0.25 = 1.69.

x ^ 2 = 1.44.

x = 1.2 dm.

Determining the area of ​​a trapezoid
To determine the area of ​​the trapezoid, we use the following formula:

S = 1/2 * (M1 + M2) * H,

Where:

S is the area of ​​the trapezoid;
M1 – smaller base;
M2 – larger base;
H is the height.
Substitute the known values ​​and get:

S = 1/2 * (6 + 2) * 1.2.

S = 1/2 * 8 * 1.2 = 4 * 1.2 = 4.8 dm ^ 2.

Answer:

The area of ​​the trapezoid is 4.8 dm ^ 2.