Area of Shapes 3

Years

Year 10

Area

Area of Shapes

Area of Shapes 3

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Question 1 of 6

Find the area of the Triangle

$\text(Area )=$ (6.975) $cm^2$

Question 2 of 6

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

Great Work!

Incorrect

Area of a Square Formula

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

In a regular square, all sides are equal

Identify the known lengths

$\text(side)=5$

Solve for the area using the Area of a Square formula

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

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

$=$ $25$

$\text(Area)=25 cm^2$

Question 3 of 6

Find the area of the Trapezium

$\text(Area ) =$ (49.77) $cm^2$

Question 4 of 6

The area of the trapezium below is:

$226.8 m^2$
Find the missing length

$? m$

The answer should be in metres.

Round your answer to one decimal place.

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

Incorrect

Area of a Trapezium Formula

$\text(Area)$

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

$times ($ $\text(base)_1$

$+$ $\text(base)_2$

$)$

Identify the known lengths

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

$\text(base)_1=? m$

$\text(base)_2=21.9 m$

$\text(height)=14 m$

Substitute the known values to the Area of a Trapezium formula

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

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

$226.8$	$=$	$(14(\text(base)_1 + 21.9))/2$	Change to quotient form

Finally, get

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

$226.8$	$=$	$(14(\text(base)_1 + 21.9))/2$

$226.8$ $times2$	$=$	$(14(\text(base)_1 + 21.9))/2$ $times2$	Multiply both sides by $2$

$226.8$ $times2$	$=$	$(2xx[14(\text(base)_1 + 21.9)])/2$

$453.6$	$=$	$14(\text(base)_1 + 21.9)$	The coefficient $2/2$ cancels out

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

$\text(?)=10.5 m$

Question 5 of 6

5. Question
Find the area of the Kite
- $\text(Area )=$ (10.5) $mm^2$
Correct

Correct!

Incorrect

Area of a Kite Formula

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

Identify the known lengths

$\text(base)=3$

$\text(height)=7$

Solve for the area using the Area of a Kite formula

$\text(Area)$ $=$ $1/2 times$ $\text(base)$ $times$ $\text(height)$ Area of a Kite formula

$=$ $1/2 times$ $3$ $times$ $7$ Plug in the known lengths

$=$ $10.5 mm^2$

The given measurements are in millimetres, so the area is measured as square millimetres

$\text(Area)=10.5 mm^2$
Question 6 of 6

6. Question
Find the missing measurement of the Parallelogram
- $h =$ (33) $km$
Correct

Nice Job!

Incorrect

Area of a Parallelogram Formula

$\text(Area)$ $=$ $\text(base)$ $xx \text(height)$

Identify the known lengths

$\text(Area)=1650 km^2$

$\text(base)=50 km$

To find the missing measurement, $h$ , solve using the Parallelogram formula and get $h$ by itself.

Substitute the known values to the Area of a Parallelogram formula

$\text(Area)$ $=$ $\text(base)$ $times \text(height)$

$1650$ $=$ $50$ $timesh$

$1650$ $=$ $50h$

Finally, divide both sides of the equation by $50$ to get the value of $h$

$1650$ $divide50$ $=$ $50h$ $divide50$

$1650$ $divide50$ $=$ $50$ $h$ $divide50$ $times50divide50$ cancels out

$33$ $=$ $h$

$h$ $=$ $33 km$

$h=33 km$

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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

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

	$=$	$1/2 times$ $4.5$ $times$ $3.1$	Plug in the known lengths

	$=$	$6.975 cm^2$

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

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

$1650$ $divide50$	$=$	$50h$ $divide50$
$1650$ $divide50$	$=$	$50$ $h$ $divide50$	$times50divide50$ cancels out
$33$	$=$	$h$
$h$	$=$	$33 km$