Question

ABCD is a square of side 7 cm. A semicircle is drawn on side AD. The perimeter of the figure is ______.

Options

• 32 cm

• 43 cm

• 50 cm

• 39 cm

Answer 1

ABCD is a square of side 7 cm. A semicircle is drawn on side AD. The perimeter of the figure is 32 cm.

Explanation:

The figure consists of a square ABCD with side 7 cm and a semicircle drawn on side AD.

1. Side of the square = 7 cm

2. Length of AD = 7 cm  ...(Side of square)

3. The perimeter of the figure will include:

• Three sides of the square (AB, BC, CD) each 7 cm
• The curved boundary of the semicircle on AD

4. Perimeter of square excluding side AD = 3 × 7 = 21 cm

5. Radius of semicircle = `"AD"/2`

= `7/2`

= 3.5 cm

6. Circumference of a full circle with radius 3.5 cm

= 2πr 

= `2 xx 22/7 xx 3.5` 

= 22 cm

7. Circumference of the semicircle

= Half the full circle

= `22/2`

= 11 cm

8. Total perimeter

= 21 cm (three sides) + 11 cm (semicircle) 

= 32 cm