5.(a) In the following triangle ABC, AB=8cm, BC=11.3cm and angle ABC=30⁰. Find area of triangle ABC.

Find he perimeter of a regular hexagon inscribed in a circle whose radius is 100 m.

Given that triangle ABC is similar to triangle PQR, AB = 4 cm, BC =5 cm, PQ = 18 cm and angle PQR is 30, find the area of triangle PQR.

  In the following figure, a regular hexagon is inscribed in a circle. If the perimeter of the  hexagon is 42 cm, find:

(a) The radius of the circle.

(b) The area of the circle and the regular polygon. 

(c)The area of the shaded region.

The areas of two similar polygons are 27 and 48 square metres. If the length of one side of the smaller polygon is 4.5 cm, find the length of the corresponding side of the larger polygon.

Two triangles are similar. A side of one triangle is 10 cm long while the length of the corresponding side of the other triangle is 18 cm. If the given sides are the bases of the triangles and the area of the smaller triangle is 40 cm² , find the area and the height of the larger triangle.

The exterior and interior angles of a regular polygon are in the ratio 2:4 respectively. Find the number of sides of the polygon.

A regular Hexagon is inscribed in a circle if the perimeter of the hexagon Is 42cm, find the radius of the circle and its Area

The area of the triangle ABC is 140 cm², AB = 20, AC = 14cm, find the angle BAC

Triangle XYZ is similar to triangle ABC and XY = 8 cm. If the area of the triangle XYZ is 24 cm² and the area of the triangle ABC is 96 cm². Calculate the length of AB.

Given that XY = 2cm, BC = 3cm and area of XYCB = 10cm³ , calculate the area of triangle AXY .

Determine the length of one side of a regular quadrilateral inscribed in a circle of radius 10cm.

The length of two sides of a triangle are 16cm and 20cm. Find the area of the triangle if the included angle is 30° .

The perimeter of a regular hexagon inscribed in a circle is 72cm. Find radius of the circle

The area of a triangle ABC is 70cm². If AB= 14cm and AC=20cm,   find the angle BAC