Area of Shapes 3

Topics

Pre - Algebra

Area

Area of Shapes

Area of Shapes 3

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Question 1 of 6

Find the area of the Triangle

$Area =$ $\text(Area )=$ (6.975) $c m^{2}$ $cm^2$

Question 2 of 6

2. Question
Find the area of the Square
- $Area =$ $\text(Area )=$ (25) $c m^{2}$ $cm^2$
Correct

Great Work!

Incorrect

Area of a Square Formula

$Area =$ $\text(Area )=$ $side$ $\text(side)$ $\times$ $times$ $side$ $\text(side)$

In a regular square, all sides are equal

Identify the known lengths

$side = 5$ $\text(side)=5$

Solve for the area using the Area of a Square formula

$Area$ $\text(Area)$ $=$ $=$ $side$ $\text(side)$ $\times$ $times$ $side$ $\text(side)$ Area of a Square formula

$=$ $=$ $5$ $5$ $\times$ $times$ $5$ $5$ Plug in the known lengths

$=$ $=$ $25$ $25$

$Area = 25 c m^{2}$ $\text(Area)=25 cm^2$

Question 3 of 6

Find the area of the Trapezium

$Area =$ $\text(Area ) =$ (49.77) $c m^{2}$ $cm^2$

Question 4 of 6

The area of the trapezium below is:

226.8 m^{2}

$226.8 m^2$
Find the missing length

? m

$? m$

The answer should be in metres.

Round your answer to one decimal place.

$? =$ $\text(?) =$ (10.5) $m$ $m$

Incorrect

Area of a Trapezium Formula

$Area$ $\text(Area)$

= \frac{1}{2} \times

$=1/2 times$ $height$ $\text(height)$

\times (

$times ($ ${base}_{1}$ $\text(base)_1$

+

$+$ ${base}_{2}$ $\text(base)_2$

)

$)$

Identify the known lengths

$Area = 226.8 m^{2}$ $\text(Area)=226.8 m^2$

${base}_{1} = ? m$ $\text(base)_1=? m$

${base}_{2} = 21.9 m$ $\text(base)_2=21.9 m$

$height = 14 m$ $\text(height)=14 m$

Substitute the known values to the Area of a Trapezium formula

$\color{#9a00c7}{\text{Area}}$	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $height$ $\text(height)$ $\times ($ $times ($ ${base}_{1}$ $\text(base)_1$ $+$ $+$ ${base}_{2}$ $\text(base)_2$ $)$ $)$	Area of a Trapezium formula

$\color{#9a00c7}{226.8}$	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $14$ $14$ $\times ($ $times ($ ${base}_{1}$ $\text(base)_1$ $+$ $+$ $21.9$ $21.9$ $)$ $)$	Plug in the known lengths

$226.8$ $226.8$	$=$ $=$	$\frac{14 ({base}_{1} + 21.9)}{2}$ $(14(\text(base)_1 + 21.9))/2$	Change to quotient form

Finally, get

{base}_{1}

$\text(base)_1$ on one side of the equation to get its value

$226.8$ $226.8$	$=$ $=$	$\frac{14 ({base}_{1} + 21.9)}{2}$ $(14(\text(base)_1 + 21.9))/2$

$226.8$ $226.8$ $\times 2$ $times2$	$=$ $=$	$\frac{14 ({base}_{1} + 21.9)}{2}$ $(14(\text(base)_1 + 21.9))/2$ $\times 2$ $times2$	Multiply both sides by $2$ $2$

$226.8$ $226.8$ $\times 2$ $times2$	$=$ $=$	$\frac{2 \times [14 ({base}_{1} + 21.9)]}{2}$ $(2xx[14(\text(base)_1 + 21.9)])/2$

$453.6$ $453.6$	$=$ $=$	$14 ({base}_{1} + 21.9)$ $14(\text(base)_1 + 21.9)$	The coefficient $\frac{2}{2}$ $2/2$ cancels out

$453.6$ $453.6$ $\div 14$ $divide14$	$=$ $=$	$14 ({base}_{1} + 21.9)$ $14(\text(base)_1 + 21.9)$ $\div 14$ $divide14$	Divide both sides by $14$ $14$
$453.6$ $453.6$ $\div 14$ $divide14$	$=$ $=$	$14$ $14$ $({base}_{1} + 21.9)$ $(\text(base)_1 + 21.9)$ $\div 14$ $divide14$	$\times 14 \div 14$ $times14divide14$ cancels out
$32.4$ $32.4$	$=$ $=$	${base}_{1} + 21.9$ $\text(base)_1 + 21.9$
$32.4$ $32.4$ $- 21.9$ $-21.9$	$=$ $=$	${base}_{1} + 21.9$ $\text(base)_1 + 21.9$ $- 21.9$ $-21.9$	Subtract $21.9$ $21.9$ from both sides
$32.4$ $32.4$ $- 21.9$ $-21.9$	$=$ $=$	${base}_{1}$ $\text(base)_1$ $+ 21.9$ $+21.9$ $- 21.9$ $-21.9$	$21.9 - 21.9$ $21.9-21.9$ cancels out
$10.5$ $10.5$	$=$ $=$	${base}_{1}$ $\text(base)_1$
${base}_{1}$ $\text(base)_1$	$=$ $=$	$10.5 m$ $10.5 m$
$?$ $\text(?)$	$=$ $=$	$10.5 m$ $10.5 m$

? = 10.5 m

$\text(?)=10.5 m$

Question 5 of 6

Find the area of the Kite

$Area =$ $\text(Area )=$ (10.5) $m m^{2}$ $mm^2$

Question 6 of 6

Find the missing measurement of the Parallelogram

$h =$ $h =$ (33) $k m$ $km$

$Area$ $\text(Area)$	$=$ $=$	$base$ $\text(base)$ $\times height$ $times \text(height)$
$1650$ $1650$	$=$ $=$	$50$ $50$ $\times h$ $timesh$
$1650$ $1650$	$=$ $=$	$50 h$ $50h$

$1650$ $1650$ $\div 50$ $divide50$	$=$ $=$	$50 h$ $50h$ $\div 50$ $divide50$
$1650$ $1650$ $\div 50$ $divide50$	$=$ $=$	$50$ $50$ $h$ $h$ $\div 50$ $divide50$	$\times 50 \div 50$ $times50divide50$ cancels out
$33$ $33$	$=$ $=$	$h$ $h$
$h$ $h$	$=$ $=$	$33 k m$ $33 km$

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Quiz summary

Information

1. Question

Keep Going!

Area of a Triangle Formula

Identify the known lengths

2. Question

Great Work!

Area of a Square Formula

Identify the known lengths

3. Question

Excellent!

Area of a Trapezium Formula

Identify the known lengths

4. Question

Correct!

Area of a Trapezium Formula

Identify the known lengths

5. Question

Correct!

Area of a Kite Formula

Identify the known lengths

6. Question

Nice Job!

Area of a Parallelogram Formula

Identify the known lengths

Quizzes

$Area$ $\text(Area)$	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $base$ $\text(base)$ $\times$ $times$ $height$ $\text(height)$	Area of a Triangle formula

	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $4.5$ $4.5$ $\times$ $times$ $3.1$ $3.1$	Plug in the known lengths

	$=$ $=$	$6.975 c m^{2}$ $6.975 cm^2$

$Area$ $\text(Area)$	$=$ $=$	$side$ $\text(side)$ $\times$ $times$ $side$ $\text(side)$	Area of a Square formula
	$=$ $=$	$5$ $5$ $\times$ $times$ $5$ $5$	Plug in the known lengths
	$=$ $=$	$25$ $25$