AREA/PREMTER/VOLUME 3

Question

Find the area and perimeter of each of the following objects. Give answers to 2 decimal places if needed. 
A) A rectangle, 3.7 cm by 8.4 cm
B) A circle with a radius of 5 m
C) A parallelogram with pairs of sides 23 mm and 17 mm long, and the distance between the long sides is 15 mm
D) A right-angled triangle in which the sides that make the right angle are 8 m and 5 m long.

Answer 1

A. Let L = length of the rectangle = 3.7 cm and W = 8.4 cm width of the rectangle.

 

  Area:  A = L * W = 31.08 cm²

  Perimeter: P = 2*(L + W) = 24.2 cm

 

B. Let r = 5 m radius of circle.

 

   Area: A = π * r² = 25π ≈ 78.54 m²

   Circumference: C = 2πr = 10π = 31.42 m

   Circumference is the perimeter for a circle.

 

C. Let the sides be s₁ = 23 mm and s₂ = 17 mm and h^₁ = 15 mm

    h₁ is the altitude to the longer side, which is s₁

 

   Area: A = s₁*h₁ = 345 mm²

   Perimeter: P = 2*(s₁ + s₂) = 80 mm

 

D. Let a = 8 m and b = 5 m

     The third side c (hypotenuse) can be found using Pythagoras' Theorem:

        c² = a² + b² = 89 => c =√89

 

     Area: A = 1/2 * a * b = 20 m²

     Perimeter:  P = a + b + c = 13 + √89 ≈ 22.43 m