Grade 5 Maths Worksheet - Geometry

Posted by Olympiad Tester on Jun 11, 2024

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 cm²

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 cm²

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

Ans: _______________________

Answer

37.5 cm²

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

Ans: _________________cm²

Answer

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 cm²

Q9) Find the area of the triangle below.

Ans: _____________cm²
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 cm²?

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

185cm²

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: _____________ cm²
Answer
324 cm²

Q16) Find the area of the shaded figure.

Answer: ___________________cm²

Answer

35 cm²

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: __________cm²

Answer

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

Ans: ___________cm²

Answer

80 cm²

Q20) The area of the rectangle ABCD below is 140 cm². Area of triangle XYD is 20 cm². Find the total shaded area of the rectangle.

Answer: ______________________________cm²

Answer

50 cm²

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: ___________________ cm²

Answer

The area of the shaded portion is 87 cm²

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

Ans: ________________ cm²
Answer
The area of triangle EFH is 21.58 cm².

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: _______________ cm²

Answer

The area of the shaded triangle is 1260 cm²

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: _______________ cm²

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: ____________ cm²

Answer

99 cm²

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 cm²

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

Ans: ________________°

Answer

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

Ans: ____________________

Answer

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

Answer

68 cm²

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: ________________m²

Answer

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

Ans: _______________cm²

Answer

Q34) The figure as shown below is made up of 6 identical triangles. If the area of the figure is 126 cm² 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: __________

Answer
13.5cm²

Q36) ABC is an equilateral triangle. ACD is an isosceles triangle. Find ∠ y.

Ans: __________ °

Answer
150°

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: __________

Answer
336 m²

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: ___________
Answer
Triangles: 17
Pentagons: 12

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

Ans:______________°

Answer

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 cm²

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

Ans:______________ cm²

Answer

Q46) The figure below is made up of equilateral triangles of different sizes.

Find the area of the shaded equilateral triangle.

Ans:______________

Answer
148 cm²