A/P/V Question 4

Question

Find the areas of the shaded portions of the figures below. Give answers to 2 decimal places if necessary.

 

A)Circle in a square (shaded part) with sides of W=10cm and L=10cm

 

B) Two triangles (shaded part) in a rectangle with:

W= 10CM

L=20CM

Answer 1

A. Assuming the shaded is the part of the square not including the circle.

 

    Since the length of the square is 10 cm, its area A_s = 10² = 100 cm²

 

   The circle has diameter that is equal to the length of the square.

   Then the radius of the circle is 5 cm, A_c = π * 52 = 25π cm²

 

   The area of the shaded area is A_s - A_c = 100 - 25π = 21.46 cm²

 

B. From the description in the comment...

 

   Let h be the altitude of one of the triangles.  Assuming the triangles touch each other

   the altitude of the other triangle would be (10 - h).

 

   The area of triangle 1 is A_T1 = (1/2) * 20 h and A_T2 = (1/2) * 20 * (10 - h)

   The combined areas of the triangles A_T = A_T1 + A_T2

                                                            = 10h + 10(10 - h) = 100 cm²

 

   This is the area of the shaded area.

 

  This is assuming the triangles lay are the side as the length of the rectangle.

  This area is also the same when the triangles lay on the same of the width.