Question

Use all the tools you have to find the perimeter and area of each shape below​

Answer 1

9514 1404 393

Answer:

1. area: 51.59 in²; perimeter: 30 in
2. area: 54 cm²; perimeter: 32.49 cm
3. area: 30 ft²; perimeter: 28 ft

Step-by-step explanation:

1. The figure can be decomposed into a square and an equilateral triangle. Both have the same side length: 6 in. For an equilateral triangle of side length s, the area is ...

  A = (√3)/4·s²

For a square with side length s, the area is ...

  A = s²

The total of the two areas is ...

  A = ((√3)/4 + 1)s² ≈ 1.433013×(6 in)²

  A ≈ 51.59 in²

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The perimeter is the sum of the 5 equal side lengths:

  P = 5(6 in)

  P = 30 in

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2. The hypotenuse of the isosceles right triangle at the top of the figure tells you the side length of the triangle is (6√2)/√2 = 6 cm. The area of the triangle is half that of the square below it, so the total area is ...

  A = (1 +1/2)(6 cm)²

  A = 54 cm²

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The perimeter is the equivalent of 4 sides of 6 cm and one of 6√2 cm, so is ...

  P = (4 +√2)(6 cm)

  P ≈ 32.49 cm

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3. The triangle at the left end of the figure has a hypotenuse of 5 and a height of 3. It is recognizable as a 3-4-5 right triangle, so the bottom leg of it is 4 ft long. That makes the bottom side of the trapezoid have a length of 8+4 = 12 ft.

The area of the trapezoid is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(12 ft +8 ft)(3 ft)

  A = 30 ft²

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The perimeter is the sum of the side lengths. Starting at left and working clockwise, that sum is ...

  P = (5 + 8 + 3 + 12) ft

  P = 28 ft

Answer 2

Answer:

Step-by-step explanation:

1)  

Area) =  area of square + area of triangle

square = 6*6 = 36  

area of equilateral triangle =   ($\sqrt{3}$ / 4) *a^2 = 31.1759

total area = 36 + 31.1759 = 67.1769$in^{2}$

Perimeter) 6*5 = 30 "

2)

Area)  = upper triangle + lower square

6*$\sqrt{2}$ *sin(45) = 6 cm ( each side is 6)

upper triangle = 1/2*6*6 = 18

lower square = 6*6=36

total area = 38 + 18 = 56 $cm^{2}$

perimeter = 4*6+6*$\sqrt{2}$ = 32.4852 cm

3)

Area) = left triangle + right rectangle

left triangle = 1/2*3*4   = 6    ( this is the famous 3,4,5 triangle )

rectangle = 8*3 = 24

total area = 24+6=30 $ft^{2}$

perimeter = 8+5+3+8+3= 27'