No questions found
(a) [Image_1: Right-angled triangle on a 1 cm² grid]
This right-angled triangle is drawn on a 1 cm² 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) [Image_2: Right-angled triangle with sides 6, 8, 10]
(i) Find the perimeter of this triangle. [2]
(ii) Find the area of this triangle. [2]
(c) [Image_3: Right-angled triangle with sides b, h, w]
Complete the table for right-angled triangles with sides $b$, $h$ and $w$.
[Table_1: Table with columns b, h, w, Perimeter P, Area A]
| b | h | w | Perimeter, $P$ | Area, $A$ |
|----|----|----|----------------|-----------|
| 12 | 5 | 13 | 30 | 30 |
| 84 | 13 | 85 | | |
| 24 | | 25 | 56 | 84 |
| 60 | 11 | | 132 | | [5]
599
569
548
(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.
(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.
550
570
569
(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) [Image_1: A right-angled triangle with $w$, $h$, $b$. Pythagoras' Theorem $w^2 = b^2 + h^2$]
Use your expression from part (b) to find the area of this triangle. .................................................. [4]
555
536
549
(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]
587
591
594
