Figure (1) is parallelogram
⇒ sides 10 , 15 and the height to the base (15) = 8
Perimeter = sum of all sides = 2 ( 10 + 15 ) = 50 m
Area = (base) * (height to this base) = 15 * 8 = 120 m²
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figure (2) is a square
The side of the square = x = 1.6 cm
Perimeter = 4 * x = 4 * 1.6 = 6.4 cm
Area = x² = 1.6² = 2.56 cm²
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Figure (3) is a triangle
The sides of the triangles are 22 , 34 , x
where x is the hypotenuse of the right triangle of sides 8 , 16
∴ x =√(8² + 16²) ≈ 17.9
perimeter of shaded triangle = 22 + 34 + 17.9 = 73.9
Area = 0.5 * base * height = 0.5 * 22 * 16 = 176
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Figure (4) is an isosceles triangle with base = 24 and height = 28
the other two sides ⇒ each one of them is the hypotenuse of the right triangle with legs = 28 , (24/2) = 12
the two equal sides = √(28² + 12²) ≈ 30.5
perimeter = 24 + 30.5 + 30.5 = 85
Area = 0.5 * base * height = 336
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figure (5) is a circle with a diameter = 88 m
∴ radius of the circle = r = 0.5 diameter = 0.5 * 88 = 44
Perimeter of the circle = 2π r = 2 * π * 44 ≈ 276.46 m
Area of the circle = π r² = π * 44² ≈ 6,082.12 m²
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figure (6) is composite of a rectangle and half of a circle
rectangle dimensions are = 15 , 34 ft & the diameter of the half of the circle = 15 ft So, the radius will be equal 15/2 = 7.5
perimeter = 3 sides of rectangle + perimeter of the half of the circle
= ( 34 + 15 + 34 ) + π * 7.5 ≈ 106.56
Area = area of the rectangle + area of the half of the circle
= ( 15 * 34 ) + 0.5 * π * 7.5² ≈ 598.36
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Figure (7): See the attached figure
composite of a rectangle in the middle and two squares on the sides
each one of the squares has a side of length = 5 ( side with double dash sign)
one sides of the rectangle has length = 5 ( side with double dash sign)
The other side of the rectangle = 3 + 5 + 2 = 10
∴ the dimensions of the rectangle are 5 , 10
Total area of the figure = area of rectangle + two times the area of one square
= 5 * 10 + 2 * 5² = 100
perimeter = the length of outer border =
= perimeter of two squares + perimeter of the rectangle - 2*( 5 + 3)
= 2 * (4 * 5) + 2 ( 5 + 10 ) - 2*( 5 +3 ) = 54
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Figure (8) is a trapezoid
the bases of the trapezoid = 18 , 30 ft and the height = 16 ft
Area = 0.5 * sum of bases * height = 0.5 * ( 18 + 30 ) * 16 = 384 ft²
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Figure (9) is a trapezoid
the bases of the trapezoid = 18 , 40 m and the height = 15 m
Area = 0.5 * sum of bases * height = 0.5 ( 18 + 40 ) * 15 = 435 m²
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Figure (10) is composite of two similar trapezoids
each of trapezoid have bases = 20 , 40 m
the height of each trapezoid = 64/2 = 32 m
the area of one trapezoid = 0.5 * sum of bases * height = 0.5 * ( 20 + 40) * 32 = 960
The total area = area of the two trapezoids = 2 * 960 =1,920 m²
