Perimeter and Area: Additional Practice (Set 1)

Area of a triangle is half the base times the height.

$A = \frac{1}{2} \times 16 \times 11 = \frac{1}{2} \times 176 = 88 \text{ cm}^2$

Subtract the removed rectangle from the full rectangle.

$10 \times 8 = 80 \text{ cm}^2, \qquad 4 \times 3 = 12 \text{ cm}^2$

$A = 80 - 12 = 68 \text{ cm}^2$

Average the parallel sides, then multiply by the height.

$\frac{9 + 15}{2} = \frac{24}{2} = 12 \text{ m}$

$A = 12 \times 10 = 120 \text{ m}^2$

A square centimetre is a square $10 \text{ mm}$ on each side, so square the factor.

$1 \text{ cm}^2 = 10 \times 10 = 100 \text{ mm}^2$

Subtract the triangle's area from the rectangle's area.

$A_{\text{rect}} = 12 \times 10 = 120 \text{ m}^2, \qquad A_{\text{tri}} = \frac{1}{2} \times 12 \times 5 = 30 \text{ m}^2$

$120 - 30 = 90 \text{ m}^2$

Find each rectangle's area, then add.

$5 \times 12 = 60 \text{ cm}^2, \qquad 7 \times 4 = 28 \text{ cm}^2$

$A = 60 + 28 = 88 \text{ cm}^2$

Convert the lengths to centimetres first: $80 \text{ mm} = 8 \text{ cm}$ and $50 \text{ mm} = 5 \text{ cm}$.

$A = 8 \times 5 = 40 \text{ cm}^2$

(In millimetres it is $80 \times 50 = 4{,}000 \text{ mm}^2$, and $4{,}000 \div 100 = 40 \text{ cm}^2$, which matches.)

Use $A = \tfrac{1}{2}(a + b)h$. The average of the parallel sides is $\tfrac{8 + 10}{2} = 9 \text{ cm}$, so $A = 9h$.

$9h = 90 \;\Rightarrow\; h = \frac{90}{9} = 10 \text{ cm}$

Trim follows the boundary, so use the perimeter.

$P = 2(30 + 20) = 2 \times 50 = 100 \text{ cm}$

$\text{cost} = 100 \times 0.20 = 20$

So the trim costs $20$ dollars.

A rhombus is a parallelogram, so its area is base times the perpendicular height. Any side serves as the base.

$A = b \times h = 6 \times 5 = 30 \text{ cm}^2$

The big square has area $9^2 = 81 \text{ cm}^2$, split into nine equal parts.

$\frac{81}{9} = 9 \text{ cm}^2$

Each small square is $3 \text{ cm}$ on a side, and $3^2 = 9 \text{ cm}^2$ agrees.

Find each area, then subtract.

$6^2 = 36 \text{ cm}^2, \qquad 4^2 = 16 \text{ cm}^2$

$36 - 16 = 20 \text{ cm}^2$