Area of a trapezoid

16-10=6

The lengths of the bases circled in red sum to 6 \, m.

So the length of one base is half of 6.

6 \div 2=3

The length of one base is 3 \, m.

Decompose the trapezoid into a rectangle and a triangle.

The area of the rectangle is:

\begin{aligned}& A=b \times h \\\\ & \text { base }=14 \\\\ & \text { height }=20 \\\\ & A=14 \times 20 \\\\ & A=280 \mathrm{~cm}^2\end{aligned}

The area of the triangle is:

\begin{aligned}& A=\cfrac{1}{2} \times b \times h \\\\ & \text { base }=4 \\\\ & \text { height }=20\end{aligned}

\begin{aligned}& A=\cfrac{1}{2} \times 4 \times 20 \\\\ & A=40 \mathrm{~cm}^2\end{aligned}

To find the area of the trapezoid, add the area of the rectangle and the area of the triangle, 40+280=320.

The area of the trapezoid is 320 \mathrm{~cm}^2.

OR

You can use the formula for the area of a trapezoid.

\begin{aligned}& \text { Area of trapezoid }=\cfrac{1}{2} \times h \times(\text { base } 1+\text { base } 2) \\\\ & \text { height }=20 \\\\ & \text { base } 1=14 \\\\ & \text { base } 2=18 \\\\ & \text { Area of trapezoid }=\cfrac{1}{2} \times 20 \times(14+18) \\\\ & \text { Area of trapezoid }=10 \times 32 \\\\ & \text { Area of trapezoid }=320 \mathrm{~cm}^2\end{aligned}

Decompose the trapezoid into one rectangle with dimensions, \text { base }=7 and the \text { height }=4.5.

The area of the rectangle is:

\begin{aligned} A=b \times h \\\\ \text { base }=7 \end{aligned}

\begin{aligned}& \text { height }=4.5 \\\\ & A=7 \times 4.5 \\\\ & A=31.5 \end{aligned}

The two triangles are congruent, where the height of the triangles is 4.5 and the base of one of the triangles can be found by:

The area of a triangle:

\begin{aligned}& \text { base }=1 \\\\ & \text { height }=4.5 \\\\ & A=\cfrac{1}{2} \times 4.5 \times 1 \\\\ & A=2.25\end{aligned}

Both triangles are equal so the area of the two triangles is, 2 \times 2.25=4.5

To find the area of the trapezoid, add the area of the rectangle and the two triangles.

\begin{aligned}& A=31.5+4.5 \\\\ & A=36 \mathrm{~m}^2\end{aligned}

OR

You can use the formula for the area of a trapezoid.

\begin{aligned}& \text { Area of trapezoid }=\cfrac{1}{2} \times h \times(\text { base } 1+\text { base } 2) \\\\ & \text { height }=4.5 \\\\ & \text { base } 1=7 \\\\ & \text { base } 2=9 \\\\ & \text { Area of trapezoid }=\cfrac{1}{2} \times 4.5 \times(7+9) \\\\ & \text { Area of trapezoid }=2.25 \times 16 \\\\ & \text { Area of trapezoid }=36 \mathrm{~m}^2\end{aligned}

First convert base 2 into centimeters by multiplying 0.68 \times 100=68.

0.68 \mathrm{~cm}=68 \mathrm{~m}

You can decompose the trapezoid into a triangle and a rectangle to find the area (see below) or use the formula for finding the area of a trapezoid,

\text { A }=\cfrac{1}{2} \times h \times(\text { base } 1+\text { base } 2)

Area of rectangle:

\begin{aligned}& A=b \times h \\\\ & \text { base }=45 \\\\ & \text { height }=90 \\\\ & A=45 \times 90 \\\\ & A=4050\end{aligned}

Area of triangle:

\begin{aligned}& A=\cfrac{1}{2} \times b \times h \\\\ & \text { base }=23 \\\\ & \text { height }=90 \\\\ & A=\cfrac{1}{2} \times 23 \times 90 \\\\ & A=1035\end{aligned}

\begin{aligned}& \text { Area of trapezoid }=\text { Area of rectangle }+ \text { Area of triangle } \\\\ & \text { Area of trapezoid }=4050+1035 \\\\ & \text { Area of trapezoid }=5085 \mathrm{~cm}^2\end{aligned}

OR

\begin{aligned}& \text { Area of trapezoid }=\cfrac{1}{2} \times h \times(\text { base } 1+\text { base } 2) \\\\ & \text { height }=90 \\\\ & \text { base } 1=45 \\\\ & \text { base } 2=68 \\\\ & \text { Area of trapezoid }=\cfrac{1}{2} \times 90 \times(45+68) \\\\ & \text { Area of trapezoid }=45 \times 113 \\\\ & \text { Area of trapezoid }=5085 \mathrm{~cm}^2\end{aligned}

You can decompose the trapezoid into a rectangle and a triangle to find the area, or you can use the formula for the area of a trapezoid.

Area of rectangle:

\begin{aligned}& A=b \times h \\\\ & \text { base }=18 \cfrac{1}{8} \\\\ & \text { height }=9 \cfrac{3}{4} \\\\ & A=18 \cfrac{1}{8} \times 9 \cfrac{3}{4} \\\\ & A=\cfrac{145}{8} \times \cfrac{39}{4} \\\\ & A=\cfrac{5655}{32} \\\\ & A=176 \cfrac{23}{32}\end{aligned}

Area of triangle:

\begin{aligned}& A=\cfrac{1}{2} \times b \times h \\\\ & \text { base }=18 \cfrac{1}{8} \\\\ & \text { height }=3 \cfrac{1}{4} \\\\ & A=\cfrac{1}{2} \times 18 \cfrac{1}{8} \times 3 \cfrac{1}{4} \\\\ & A=\cfrac{1}{2} \times \cfrac{145}{8} \times \cfrac{13}{4} \\\\ & A=\cfrac{1885}{64} \\\\ & A=29 \cfrac{29}{64}\end{aligned}

\begin{aligned}& \text { Area of trapezoid }=\text { Area of rectangle }+ \text { Area of triangle } \\\\ & \text { Area of trapezoid }=176 \cfrac{23}{32}+29 \cfrac{29}{64} \\\\ & \text { Area of trapezoid }=176 \cfrac{46}{64}+29 \cfrac{29}{64} \\\\ & \text { Area of trapezoid }=205 \cfrac{75}{64}=206 \cfrac{11}{64} \mathrm{~in}^2\end{aligned}

OR

\begin{aligned}& \text { Area of trapezoid }=\cfrac{1}{2} \times h \times(\text { base } 1+\text { base } 2) \\\\ & \text { height }=18 \cfrac{1}{8} \\\\ & \text { base } 1=9 \cfrac{3}{4} \\\\ & \text { base } 2=13 \\\\ & A=\cfrac{1}{2} \times 18 \cfrac{1}{8} \times\left(9 \cfrac{3}{4}+13\right) \\\\ & A=\cfrac{1}{2} \times 18 \cfrac{1}{8} \times 22 \cfrac{3}{4} \\\\ & A=\cfrac{1}{2} \times \cfrac{145}{8} \times \cfrac{91}{4} \\\\ & A=\cfrac{13195}{64}=206 \cfrac{11}{64} \mathrm{~in}^2\end{aligned}

The formula for the area of a trapezoid is:

\begin{aligned}& \text { Area }=\cfrac{1}{2} \times h \times(\text { base } 1+\text { base } 2) \\\\ & \text { Area }=54 \\\\ & \text { base } 1=6 \\\\ & \text { base } 2=9 \\\\ & 54=\cfrac{1}{2} \times h \times(6+9) \\\\ & 54=\cfrac{1}{2} \times h \times 15 \\\\ & 54=7.5 \times h \\\\ & 54 \div 7.5=7.5  \times h\div 7.5 \\\\ & 7.2=h\end{aligned}

The height of the trapezoid is 7.2 \, cm.

\begin{aligned} & \text { Area of trapezoid }=\cfrac{1}{2} \times h \times(\text { base } 1+\text { base } 2) \\\\ &\text { Area of trapezoid }=\cfrac{1}{2} \times 5 \times(6+11) \\\\ & \text { Area of trapezoid }=\cfrac{1}{2} \times 5 \times 17 \\\\ & \text { Area of trapezoid }=42.5 \mathrm{~m}^2\end{aligned}

The area of the garden is 42.5 \, m^2 and an individual roll of grass covers 4 \mathrm{~m}^2. So to find the total number of rolls of grass needed, divide the area by the area of one roll.

42.5 \div 4=10.625

Since Sally cannot buy 0.625 of a roll of grass, she will need to purchase 11 rolls of grass.