What is the area of the parallelogram?

20 √2 cm 2
40 cm 2
20 cm 2
40 √2 cm 2

20√2 cm²

Step-by-step explanation:

Area of parallelogram = base * height

base (b) = 10 cm

height (h) = ?

Apply trigonometric function to find the height (h)

Assuming the height connecting the parallel bases together forms a right angle, therefore

Reference angle = 45°

Opposite = height (h)

Hypotenuse = 4 cm

Apply SOH:

Sin 45 = Opp/Hyp

Sin 45 = h/4

4*Sin 45 = h

4*√2/2 = h (sin 45 = √2/2)

2√2 = h

h = 2√2 cm

✔️Area = base * height = 10 * 2√2

= 20√2 cm²

3 1/3 x 2 3/5 = 8 2/3

step-by-step explanation:

just multiply the first number by the second number to get your answer.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240