No questions found
(a)
This right-angled triangle is drawn on a $1 \text{ cm}^2$ grid.
(i) Measure and write down the length of the hypotenuse.
.................................................. [1]
(ii) Show that the perimeter is 12.
.................................................. [1]
(iii) Find the area of the triangle.
.................................................. [1]
(b)
(i) Find the perimeter of this triangle.
.................................................. [2]
(ii) Find the area of this triangle.
.................................................. [2]
(c)
Complete the table for right-angled triangles with sides $b$, $h$ and $w$.
| $b$ | $h$ | $w$ | Perimeter, $P$ | Area, $A$ |
|-----|-----|-----|----------------|-----------|
| 12 | 5 | 13 | 30 | 30 |
| 84 | 13 | 85 | | |
| 24 | | 25 | 56 | 84 |
| 60 | 11 | | 132 | |
513
551
588
(a)
This triangle has perimeter $P = 60$.
Show that the calculation $\frac{60}{2} \times \left(\frac{60}{2} - 26\right)$ gives the correct area for this triangle.
[3]
(b)
This triangle has perimeter $P = 112$.
Show that the calculation $\frac{112}{2} \times \left(\frac{112}{2} - 50\right)$ gives the correct area for this triangle.
[3]
551
576
525
(a) Complete the table.
[Table_1]
\begin{array}{|c|c|c|c|c|c|} \hline b & h & w & P & A & \text{Calculation} \\ \hline 24 & 10 & 26 & 60 & 120 & \frac{60}{2} \times \left(\frac{60}{2} - 26\right) = 120 \\ \hline 12 & 9 & 15 & 36 & 54 & \frac{36}{2} \times \left(\frac{36}{2} - 15\right) = 54 \\ \hline 48 & 50 & & 112 & & \frac{112}{2} \times \left(\frac{112}{2} - 50\right) = \\ \hline 15 & 8 & 17 & 60 & & = 60 \\ \hline 21 & 29 & 70 & 210 & & = \\ \hline 12 & & 37 & 210 & & = \\ \hline \end{array}
[8]
(b) Write an expression for the area of a right-angled triangle in terms of $P$ and $w$.
.......................................................... [1]
(c) 
Use your expression from part (b) to find the area of this triangle.
.......................................................... [4]
504
536
580
(a)
This is a rhombus.
Use Question 3(b) to write down an expression for the area of this rhombus in terms of $P$ and $w$. ................................................... [1]
(b) Use your expression from part (a) to find the area of this rhombus when $w = 41$ and $b = 40$. ................................................... [4]
588
571
598
