15A Core skills 1. Find (i) the area and (ii) the perimeter of the following shapes. (i)
(ii) (iii)
2. (i) Construct rectangle XYWZ, |XY| = 110 mm, |YW| = 80mm. (ii) Find the perimeter of this rectangle.
(Hint: draw a rough sketch first.) (iii) Find the area of this rectangle.
3. Identify the types of triangle shown here. Give a reason for your answer. Note: in some cases, triangles can be two different types at the same time.
(i) (ii) (iii) (iv) (v)
4. Construct the triangle ABC where |AB| = 7 cm, |BC| = 5 cm and |AC| = 6 cm. 5. Construct the triangle ABC where |AB| = 6 cm, |∠BAC| = 60° and |AC| = 8 cm. 6. Construct the triangle PQR where: |∠QPR| = 60°, |PQ| = 7·5 cm and |∠PQR| = 70°. 7. Construct the right-angled triangle ABC where |AB| is the hypotenuse, |AB| = 7 cm and |BC| = 5 cm. 8. Construct the right-angled triangle ABC where |AB| is the hypotenuse, |AB| = 9.5 cm and |∠CAB| = 47°.
9. Find the size of the angles marked with a letter in the following triangles. Write down the axiom or theorem used in each case. (i)
(ii) X 100° 47° 60° 67° Y P
10. Find the area of the shaded region in the following diagrams. (i)
(ii) 5 cm 8 cm 10 cm 4 cm 3 cm (iii) 4 cm 5 cm (iv) 3·5 cm M Y (iii) 63° N (iv) 55° 85°