Answer:
Nothing is being handed, see below.
Explanation:
To calculate the area of parallelogram EFGH and the length of the diagonal EG, we can use the given information and apply relevant formulas.
(a) Area of the parallelogram:
The area of a parallelogram can be calculated by multiplying the length of its base by its corresponding height. In this case, we can take EF as the base and find the corresponding height.
Since EF and HG are parallel sides of the parallelogram, the height of the parallelogram can be determined by drawing a perpendicular line from H to EF. Let's call the point of intersection K.
Given that angle EFG is 106 degrees, we can find angle GFE by subtracting 106 degrees from 180 degrees (as the angles in a triangle add up to 180 degrees). So, angle GFE = 180 - 106 = 74 degrees.
Now, we can use trigonometry to find the height HK. Since angle GFE is known, we can use the tangent function:
tan(GFE) = HK / FG
tan(74) = HK / 14.7
HK = 14.7 * tan(74)
Now, we can calculate the area of the parallelogram using the formula:
Area = base * height = EF * HK
Substituting the given values:
Area = 9.3 * (14.7 * tan(74))
Evaluate the expression to get the answer. The area of the parallelogram will be given in square centimeters, rounded to 3 significant figures.
(b) Length of the diagonal EG:
To find the length of diagonal EG, we can use the Pythagorean theorem. In parallelogram EFGH, EG forms a right triangle with sides EF and FG.
Using the Pythagorean theorem, we have:
EG^2 = EF^2 + FG^2
Substituting the given values:
EG^2 = 9.3^2 + 14.7^2
Solve the equation to find the value of EG. The length of the diagonal EG will be given in centimeters.