![]() Here,ī and d are parallel sides of the trapezoid The base of a trapezoidal prism is trapezoid in shape. Area of a trapezoid = ½ (a + b) h where h = 4 cm, a =10 cm b = 16 cm On substituting values we get: Area = ½ (10 + 16) × 4 Area = ½ × 26 × 4 Area = 52 cm 2 We can calculate by adding area of the rectangle and two triangles Area of trapezoid = Area of ABPQ + Area of ADP + Area of BQC Area of trapezoid = (l × b) + 2( ab/2) Area of trapezoid = (10 × 4) + 2(3 ×4/2) A = 40 + 12 A = 52 cm 2 We can calculate the area using the formula. ![]() Step 4: Now we know all the dimensions of the trapezoid. In the right-angled triangle ADP AP = √(AD 2 – DP 2) AP = √(5 2 – 3 2) AP = √(25 – 9) = √16 = 4 cm Since ABQP is a rectangle, the opposite sides will be equal. Since ABQP is a rectangle, AB = PQ DC = 16 cm (Given) So, PQ = AB We can find the combined length of DP + QC as follows DC – PQ = 16 – 10 = 6 cmSo, DP + QC = 6 6 ÷ 2 = DP = QC 3 cm = DP = QC Step 3: AP = BQ (opposite and equal sides of a rectangle) AD = BC = 5 cm (Given) So, we can calculate the height AP and BQ using Pythagoras theorem. Step 2: Now, we have to find the length of DP and QC. Now we can see that the trapezoid consists of a rectangle ABQP and 2 right-angled triangles, APD and BQC. Given: a =10 cm b =16 cm non-parallel sides = 5 cm each Step 1: To find the height of the trapezoid, we will first draw the height of the trapezoid on both sides. Solution: Since in this question, we don’t have the height of the trapezium, we will follow the following steps to calculate the area of the trapezoid. The area of the trapezoid = A = ½ (a + b) h A = ½ (22 + 10) × (5) A = ½ (32) × (5) A = ½ × 160 A = 80 cm 2Įxample 2: Find the area of a trapezoid whose parallel sides are given as 10cm and 16cm, respectively, and the non-parallel sides are 5cm each. Solution: Given: The bases are : a = 22 cm b = 10 cm the height is h = 5 cm. Example 1: Find the area of a trapezoid given the length of parallel sides 22 cm and 12 cm, respectively. Here is an area of a trapezoid example using the direct formula and an area of a trapezoid example with the alternative method. ‘h’ is the height, i.e., the perpendicular distance between the parallel sides. We can calculate the area of a trapezoid if we know the length of its parallel sides and the distance (height) between the parallel sides. What is the Formula To Calculate the Area of Trapezoids? (see example 2 for a more precise understanding) Finally, we will add the area of the polygons to get the total area of the trapezoid. ![]() Next, we will find the area of the triangles and rectangles separately.
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