Question

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

Answer 1

Explanation:

1)

Area) = area of square + area of triangle

square = 6*6 = 36

area of equilateral triangle = (
`√(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*
`√(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*
`√(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'

Answer 2

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

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