Exercise 1

Determine the area of an isosceles right triangle with the equal sides each measuring 10 cm in length.

Exercise 2

Calculate the number of trees that can be planted in a rectangular field which is 32 m long and 30 m wide if each tree needs 4 m² to grow.

Exercise 3

The area of a trapezoid is 120 m², the height is 8 m, and the smaller base measures 10 m. What is the length of the other base?

Exercise 4

Calculate the area of a parallelogram whose height is 2 cm and its base is 3 times its height.

Exercise 5

What is the area of the shaded area in the figure if the area of the entire hexagon is 96 cm²?

Exercise 6

Calculate the area of a rhombus whose larger diagonal measures 10 cm and whose minor diagonal is half the length of the other.

Exercise 7

Calculate the number of square tiles needed to cover a rectangular surface of 4 m by 3 m if the length of each side of the tiles is 10 cm.

Exercise 8

The perimeter of an equilateral triangle is 0.9 dm and its height is 25.95 cm. Calculate the area of the triangle.

Exercise 9

A rectangular field has a length of 170 m and a width of 28 m. Calculate:

1The area of the field in hectares.

2The price to re-seed the field if each square meter costs 15.</span> 				  						 </div> 					  </section><section id="am" style=""> 				 					 						 						 					  <h2>Solution of exercise 1</h2> 					  Determine the area of an isosceles <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/plane/right-triangle.html" title="right triangle" style="text-decoration:underline;">right triangle</a> with the equal sides each measuring 10 cm in length. <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/101-1561537470735-7578.gif"     > 						  						A =  (10 ·  10) : 2 = <span class="sol">50 cm² </span> 				       					      					 					  <h2>Solution of exercise 2</h2> 					  Calculate the number of trees that can be planted in a rectangular field which is 32 m long and 30 m wide if each tree needs 4 m² to grow. A =  32 ·  30 =  960 m² 					    960   : 4 = <span class="sol">240 trees </span> 					 					 					  <h2>Solution of exercise 3</h2> 					  The area of a <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/plane/trapezoids.html" title="trapezoid" style="text-decoration:underline;">trapezoid</a> is 120 m², the height is 8 m, and the smaller base measures 10 m. What is the length of the other base? <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/92_1-15615374708443-1762.gif"     > <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/92_2-15615374710238-6058.gif"     > <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/92_3-15615374711966-439.gif"     > 					 					 					  <h2>Solution of exercise 4</h2> 						Calculate the area of a <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/plane/parallelograms.html" title="parallelogram" style="text-decoration:underline;">parallelogram</a> whose height is 2 cm and its base is 3 times its height. 					  h = 2 cm 					    b = 2  · 3 = 6 cm 						A = 2 · 6 = <span class="sol">12 cm² </span>	 					 					 					  <h2>Solution of exercise 5</h2> 					  What is the area of  the shaded area   in the figure  if the area of the entire <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/plane/regular-hexagons.html" title="hexagon" style="text-decoration:underline;">hexagon</a> is 96 cm²? <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/94-15615374712888-4837.gif"     >	                       	96 :  6 = <span class="esmeralda">16 cm² </span>                         16 ·  2 = <span class="sol">32 cm² </span>		 						 					 					  <h2>Solution of exercise 6</h2> 					  Calculate the area of a <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/plane/rhombus.html" title="rhombus" style="text-decoration:underline;">rhombus</a> whose larger diagonal measures 10 cm and whose minor diagonal  is half the length of the other. D = 10 cm 					    d = 10 : 2 = 5 cm 				      	A =  (10 · 5) :  2 =  25 cm²  					 					 						 					  <h2>Solution of exercise 7</h2> 					  Calculate the number of square tiles  needed to cover a rectangular surface of 4 m by 3 m if the length of each side of the tiles is 10 cm. A<sub>S</sub> = 4  · 3 =  12 m² = 120,000 cm² 				      A<sub>B</sub> = 10 · 10 = 100 cm² 					    120,000 : 100 =  <span class="sol">1,200 tiles</span> 					                        						 					  <h2>Solution of exercise 8</h2> 					  The perimeter of an <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/plane/equilateral-triangles.html" title="equilateral triangle" style="text-decoration:underline;">equilateral triangle</a> is 0.9 dm and its height is 25.95 cm. Calculate the area of the triangle. <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/102-15615374714294-7306.gif"     >	 						P = 0.9 dm = 90 cm 						l  = 90 :  3 =  30 cm  						A =  (30 ·  25.95) : 2 = <span class="sol">389.25 cm² </span> 											   					                       						 		  <h2>Solution of exercise 9</h2> 		  A rectangular field has a length of 170 m  and a width of 28 m. Calculate: 		  <span class="numero_r">1</span>The area of the field in hectares. A =  170 ·  28 = 4,760 m²                         4,760 : 10,000 =<span class="sol"> 0. 476 ha </span>                         <span class="numero_r">2</span>The price to re-seed the field if each square meter costs15.

4,760 · 15 = $71,400

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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