# Test: Triangles - Challenging

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Question 1:   Find $\alpha$ $\alpha ={90}^{\circ }$
$\alpha ={80}^{\circ }$
$\alpha ={60}^{\circ }$
$\alpha ={75}^{\circ }$
Question 2:   Find the height of a triangle where $a=6cm$ $3$
$3\sqrt{2}$
$\sqrt{6}$
$3\sqrt{3}$
Question 3:   Find the area: $25c{m}^{2}$
$22.5c{m}^{2}$
$20c{m}^{2}$
$17.5c{m}^{2}$
Question 4:   Which set of numbers is the side lengths of a triangle?
$\sqrt{2},2\sqrt{2},3\sqrt{2}$
$\sqrt{3},\sqrt{5},5$
$2,\sqrt{5},5$
$2\sqrt{3},3\sqrt{2},\sqrt{7}$
Question 5:   Which set of numbers forms a right-angled triangle?
$3\sqrt{5},2\sqrt{5},5$
$2\sqrt{7},2\sqrt{6},\sqrt{5}$
$2\sqrt{10},3\sqrt{3},3$
$3\sqrt{2},2\sqrt{3},2\sqrt{2}$
Question 6:   Which set of numbers forms a right-angled triangle?
$7,5,3\sqrt{2}$
$2\sqrt{15},6,2\sqrt{7}$
$4\sqrt{2},3\sqrt{3},2\sqrt{14}$
$8,2\sqrt{10},2\sqrt{6}$
Question 7:   What is a side length of an equilateral triangle with the height equal to $\sqrt{3}cm$
$\sqrt{6}cm$
$2cm$
$2\sqrt{3}cm$
$3cm$
Question 8:   Find the perimeter of a square where the diagonal is equal to $5\sqrt{6}cm$
$20\sqrt{3}cm$
$44cm$
$40\sqrt{3}cm$
$75cm$
Question 9:   Find the area of a trapezium: $40c{m}^{2}$
$44c{m}^{2}$
$55c{m}^{2}$
$50c{m}^{2}$
Question 10:   Find the area of an inscribed triangle, where the radius of a circle is equal to $8cm$ $60\sqrt{3}c{m}^{2}$
$81c{m}^{2}$
$64c{m}^{2}$
$36c{m}^{2}$