What is the area of this shape?

235 cm^2

Step-by-step explanation:

First you should divide this shape into to rectangles or squares. Then you can easily find the area.

20-11=9

We have a rectangle and a square.

(11*14) + (9*9)

A = 235 cm²

Step-by-step explanation:

The figure is composed of 2 rectangles.

main rectangle has dimensions length = 20 cm , breadth = 9 cm

The attached rectangle , on top has dimensions

length = 11 cm , breadth = 14 - 9 = 5 cm

Total area (A) is the sum of the areas of the 2 rectangles

A = (20 × 9) + (11 × 5) = 180 + 55 = 235 cm²

(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

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm