Area worksheet

1. Area: 31.5 mm²

1. Average the two parallel sides, then multiply by the height between them

   $\frac{7+14}{2}\times 3$$=31.5\text{\hspace{0.17em}mm²}$

2. To change to square meters, multiply by the size of 1 mm in meters, squared, because area has two directions

   $31.5\text{\hspace{0.17em}mm²}\times {0.001}^2$$=0.000032\text{\hspace{0.17em}m²}$

2. Area: 16 cm²

1. Multiply the side by itself (side squared), since a square's length and width are the same

   $4^2$$=16\text{\hspace{0.17em}cm²}$

2. To change to square meters, multiply by the size of 1 cm in meters, squared, because area has two directions

   $16\text{\hspace{0.17em}cm²}\times {0.01}^2$$=0.0016\text{\hspace{0.17em}m²}$

3. Area: 28.27 cm²

1. Multiply π (about 3.14) by the radius squared, the radius times itself

   $\pi \times 3^2$$=28.274334\text{\hspace{0.17em}cm²}$

2. To change to square meters, multiply by the size of 1 cm in meters, squared, because area has two directions

   $28.274334\text{\hspace{0.17em}cm²}\times {0.01}^2$$=0.002827\text{\hspace{0.17em}m²}$

4. Area: 50.27 cm²

1. Multiply π (about 3.14) by the radius squared, the radius times itself

   $\pi \times 4^2$$=50.265482\text{\hspace{0.17em}cm²}$

2. To change to square meters, multiply by the size of 1 cm in meters, squared, because area has two directions

   $50.265482\text{\hspace{0.17em}cm²}\times {0.01}^2$$=0.005027\text{\hspace{0.17em}m²}$

5. Area: 34 km²

1. Average the two parallel sides, then multiply by the height between them

   $\frac{5+12}{2}\times 4$$=34\text{\hspace{0.17em}km²}$

2. To change to square meters, multiply by the size of 1 km in meters, squared, because area has two directions

   $34\text{\hspace{0.17em}km²}\times {\mathrm{1,000}}^2$$=\mathrm{34,000,000}\text{\hspace{0.17em}m²}$

6. Area: 28.27 mm²

1. Multiply π (about 3.14) by the radius squared, the radius times itself

   $\pi \times 3^2$$=28.274334\text{\hspace{0.17em}mm²}$

2. To change to square meters, multiply by the size of 1 mm in meters, squared, because area has two directions

   $28.274334\text{\hspace{0.17em}mm²}\times {0.001}^2$$=0.000028\text{\hspace{0.17em}m²}$

7. Area: 30 km²

1. Average the two parallel sides, then multiply by the height between them

   $\frac{8+12}{2}\times 3$$=30\text{\hspace{0.17em}km²}$

2. To change to square meters, multiply by the size of 1 km in meters, squared, because area has two directions

   $30\text{\hspace{0.17em}km²}\times {\mathrm{1,000}}^2$$=\mathrm{30,000,000}\text{\hspace{0.17em}m²}$

8. Area: 75.4 in²

1. Multiply π by half the longest width and half the shortest width of the ellipse (oval)

   $\pi \times 6\times 4$$=75.398224\text{\hspace{0.17em}in²}$

2. To change to square meters, multiply by the size of 1 in in meters, squared, because area has two directions

   $75.398224\text{\hspace{0.17em}in²}\times {0.0254}^2$$=0.048644\text{\hspace{0.17em}m²}$

9. Area: 16 mm²

1. Multiply the base by the height, then halve it, because a triangle is half of a rectangle that size

   $\frac{8\times 4}{2}$$=16\text{\hspace{0.17em}mm²}$

2. To change to square meters, multiply by the size of 1 mm in meters, squared, because area has two directions

   $16\text{\hspace{0.17em}mm²}\times {0.001}^2$$=0.000016\text{\hspace{0.17em}m²}$

10. Area: 26 in²

1. Average the two parallel sides, then multiply by the height between them

   $\frac{6+7}{2}\times 4$$=26\text{\hspace{0.17em}in²}$

2. To change to square meters, multiply by the size of 1 in in meters, squared, because area has two directions

   $26\text{\hspace{0.17em}in²}\times {0.0254}^2$$=0.016774\text{\hspace{0.17em}m²}$