# Grade 5 Maths Worksheet - Geometry

Posted by **Olympiad Tester** on

**Q1) In the figure below, ABCD is a rectangle.AB is 44 cm long and BC is 30 cm wide.AXC and BXD are straight lines where AX = XC and BX = XD.Express the total unshaded area as a fraction of the total shaded area.**

**Answer**

** 1/3 **

**Q2) The figure below is made up of three squares of sides 1 cm, 2 cm and 3 cm. What is its perimeter?**

Answer: _________________________

Answer

18 cm

**Q3) In the figure below, a triangle is drawn inside a rectangle. Find the area of the shaded triangle below.**

Ans: __________________

Answer

60 cm^{2}

**Q4) The figure below is made up of 4 identical rectangles. The perimeter of the figure is 216 cm. Find the area of the figure.**

Answer: _________________________

**Answer**

** 2 592 cm ^{2}**

** **

**Q5) ****The figure below, not drawn to scale, is made up of two squares. Find the shaded area.**

**Ans: _______________________**

**Answer**

** 37.5 cm ^{2} **

**Q6) ****The triangle is not drawn to scale. Find the shaded area.**

**Ans: _________________cm ^{2}**

**Answer**

** 36**

**Q7) ****In the figure below, PQ is parallel to ST. Find ∠ PQR +∠ RST.**

**Ans: _____________° **

**Answer**

** 380° **

**Q8****) In the figure below, not drawn to scale. ABCD is a rectangle. EF is 4 cm. Find the area of the shaded region.**

**Ans: _______________________**

**Answer**

** 100 cm ^{2}**

**Q9) Find the area of the triangle below.**

** **

Ans: _____________cm^{2}

Answer

75

**Q10) The figure below is not drawn to scale. What is the length of AC?**

Answer: _________________________

**Answer**

** 10 cm**

**Q11)ABGH, BCFG and CDEF are similar squares. What is the perimeter of the rectangle ADEH if the area of each square is 121 cm ^{2}?**

Ans: _____________ cm

Answer

88 cm

**Q12) ****In the figure below, ABC is a right-angled isoceles triangle. BD is a straight line. Find the value of ∠ x.**

**Ans: _____________° **

**Answer**

** 70° **

**Q13) ****The figure below is not drawn to scale. Find the shaded area.**

**Ans: _________________**

**Answer**

** 185cm ^{2}**

**Q14) In the figure below, ABC is a right-angled triangle, ACD is an isoceles triangle, AED and BEC are straight lines.**

**(a) Find ∠ ABC**

**(b) Find ∠ ADB**

**Ans: (a) _______________**

** (b) _______________**

** Answer**

**(a) ∠ ABC is 61° .**

**(b) ∠ ADB is 31° .**

**Q15) The four corners of a square piece of paper were folded inwards to form the following square below. What was the area of the paper before it was folded?**

** **

Ans: _____________ cm^{2}

Answer

324 cm^{2}

**Q16) Find the area of the shaded figure.**

Answer: ___________________cm^{2}

**Answer**

** 35 cm ^{2}**

**Q17)****At first, Julie was standing at P, facing the East. she turned 225° clockwise and then 90° anticlockwise. Which direction was she facing then?**

**Ans: _______________**

**Answer**

** south-west**

**Q18) ****The figure below is not drawn to scale. Find the area of the shaded triangle.**

**Ans: __________cm ^{2}**

**Answer**

** 42**

**Q19) ****The figure shown below is made up of two squares of different lengths. Find the area of the shaded triangle.**

**Ans: ___________cm ^{2}**

**Answer**

**80 cm ^{2}**

** **

**Q20) The area of the rectangle ABCD below is 140 cm ^{2}. Area of triangle XYD is 20 cm^{2}. Find the total shaded area of the rectangle.**

** **

Answer: ______________________________cm^{2}

**Answer**

** 50 cm ^{2}**

**Q21)** **The figure below is not drawn to scale. The breadth of the rectangle is 3/5 its length. Find the area of the shaded portion.**

**Ans: ___________________ cm ^{2}**

**Answer**

** The area of the shaded portion is 87 cm ^{2 }**

**Q22) Triangle DEF is made up of 2 triangles, EFH and DFH. Find the area of triangle EFH.**

Ans: ________________ cm^{2}

Answer

The area of triangle EFH is 21.58 cm^{2}.

**Q23)The figure shows a triangle drawn inside a square of side 60 cm. The ratio of LP to PO is 7 : 3. Find the area of the shaded triangle.**

**Ans: _______________ cm ^{2}**

**Answer**

** The area of the shaded triangle is 1260 cm ^{2 }**

**Q24) A square piece of paper has a perimeter of 60 cm. It is folded at a corner forming a shaded triangle with DC = DB. AB is 4 times as long as DC. Find the area of the unshaded part.**

**Ans: _______________ cm ^{2}**

**Answer**

^{ The area of the unshaded part is 216 cm2. }

**Q25)The figure below is not drawn to scale. QT is 24 cm long. UT = RV. Find the shaded area.**

** **

** **

**Ans: ____________ cm ^{2}**

**Answer**

** 99 cm ^{2 }**

**Q26) ****In the figure below, AOB = 2BOC and EOF = 46°. Find the K**

** **

** **

**Ans: ____________________**

**Answer**

** 164°**

**Q27) The figure below is made up of a square, a rectangle and three identical triangles. Find the area of the figure.**

** **

**Ans: ____________________**

**Answer**

** 60 cm ^{2}**

**Q28) In the figure, not drawn to scale, AB, CD and EF are straight lines. Find K.**

** **

** **

**Ans: ________________°**

**Answer**

** 58**

**Q29) ****In triangle ABC, if the height is AE, what is the base?**

**Ans: ____________________**

**Answer**

** BC**

**Q30) ****ABCD is a rectangle, What is the shaded area?**

**Answer**

** 68 cm ^{2}**

**Q31) ****What fraction of the area of the unshaded parts is the area of the shaded triangle?**

** **

** **

**Ans: ____________________**

**Answer**

** 42/174 **

**Q32) ****The perimeter of rectangle PQRS is 78 m. Find the area of the shaded triangle.**

**Ans: ________________m ^{2}**

**Answer**

** 75**

**Q33) ****Find the area of the shaded figure. (Figure not drawn to scale).**

**Ans: _______________cm ^{2}**

**Answer**

**90**

**Q34) ****The figure as shown below is made up of 6 identical triangles. If the area of the figure is 126 cm ^{2} and its perimeter is 36 cm, find the height of each triangle. (Figure not drawn to scale).**

** **

** **

**Ans: _________________**

**Answer**

** 7 cm**

**Q35) ABFG and BCDE are squares (not drawn to scale).Find the area of the shaded region.Ans: __________Answer13.5cm**

^{2}

**Q36) ABC is an equilateral triangle. ACD is an isosceles triangle. Find ∠ y.Ans: __________ ° Answer150°**

**Q37) The figure ACFD shown below is divided into 2 equal parts. AB = BC. What is the area of the shaded parts given that they are identical to each other?Ans: __________Answer336 m**

^{2}

**Q38) 45 triangles, squares and pentagons have 175 sides altogether. There are 64 sides for all the squares. How many triangles and pentagons are there?Ans: Triangles: ___________ Pentagons: ___________AnswerTriangles: 17Pentagons: 12**

**Q39) ****In the figure, not drawn to scale, AB and CD are straight lines. Find ∠ COE.**

** **

**Ans:______________° **

**75**

**Q40) ****In the figure, not drawn to scale, ∠ b=55° ∠ a is three times the size of ∠ b. Find ∠c .**

** **

** **

** Ans:______________° **

** Answer**

**140**

**Q41) The perimeter of a rectangle is 56 cm. The ratio of its length to its breadth is 5:2. Find its breadth.Ans: __________ cm**

**Answer**

** 8 cm**

**Q42)** **In the figure above, not drawn to scale, AB, PQ, and XY are straight lines. ∠ AXP is a right angle and ∠ YXQ = 54° . Find the value of ∠ BXY.**

Ans: __________°

**Answer**

** 36° **

**Q43) The figure is made up of seven similar equilateral triangles.What is the perimeter of the figure?Ans ;__________ cm**

**Answer**

** 60 cm**

**Q44) ABCD is a rectangle of sides 20 cm and 16 cm. Given that AE = EB, what is the area of the shaded part?**

Ans:______________

**Answer**

** 210 cm ^{2}**

**Q45) In triangle EFGH, FH is 12 cm. Find the area of the rectangle.Ans:______________ cm**

^{2}

**Answer**

** 48**

**Q46) The figure below is made up of equilateral triangles of different sizes.Find the area of the shaded equilateral triangle.Ans:______________ Answer148 cm**

^{2}

**Q47) The perimeter of the figure is 54 m. Find the area of the shaded part.**

Ans:_______________________m^{2}

Answer**30**

**Q48) ABCD is a rectangle 12 cm by 6 cm. BF is 4 cm. Find the area of triangle AFC.Ans:______________ cm**

^{2}Answer12

**Q49) Find the area of the shaded triangle.Ans:______________ cm**

^{2}Answer135