Problem Solving with Areas Flashcards

All 8 cards in this deck

What are the steps to find the perpendicular height of a triangle from its area?

e.g. area $24$ cm$^2$, base $8$ cm

1. Put the numbers in the formula: $\frac{1}{2}\times8\times h=24$
2. Simplify: $4h=24$
3. Divide: $h=6$ cm

How do you find the perpendicular height of a parallelogram from its area and base?

e.g. area $30$ cm$^2$, base $5$ cm

Divide the area by the base.

e.g. $30 \div 5 = 6$ cm

What are the steps when one shape's area is a given multiple of another's?

e.g. a rectangle of length 16 cm has 6 times the area of a triangle with base 8 cm and height 9 cm — find its width

1. Find the first area: $\frac{1}{2}\times8\times9=36$
2. Multiply by the given number: $6\times36=216$
3. Divide by the known length: $216\div16=13.5$ cm

What are the steps to work out the cost of covering a floor at a price per square metre?

e.g. a floor 6 m by 4 m at £3 per m$^2$

1. Find the area: $6\times4=24$ m$^2$
2. Multiply by the cost per m$^2$: $24\times3$
3. Answer: £72

What are the steps to find $x$ when the sides are given in terms of $x$ and the perimeter is known?

e.g. a rectangle with sides $x+1$ and $2x$, perimeter $26$ cm

1. Write the perimeter in terms of $x$: $2(x+1+2x)=6x+2$
2. Form an equation: $6x+2=26$
3. Solve: $x=4$

How many cm$^2$ are there in $1$ m$^2$?

$10\,000$ cm$^2$, because $1$ m $=100$ cm and $100\times100=10\,000$.

The area of shape A is 5 times the area of shape B. What equation do you write to compare them?

e.g. B is a triangle of area $72$ cm$^2$, A is a parallelogram with base $30$ cm and perpendicular height $h$

area of A $= 5 \times$ area of B

e.g. $30 \times h = 5 \times 72$

True or false? If the side length of a square is doubled, its area is doubled.

False. The area becomes $4$ times as large.