The base of a right prism is a quadrilateral ABCD, given that AB = 9 cm, BC = 14 cm, CD = 13 cm, DA = 12 cm and ∠DAB = 90°, If the volume of the prism be 2070 cm3, then what is the area of the lateral surface?Choices:- 720 cm3 810 cm3 1260 cm3 2070 cm3

To solve this problem, we first need to find the height of the prism.

Step 1: Find the area of the base of the prism. Since ∠DAB = 90°, triangle ABD is a right triangle. We can find the area of triangle ABD using the formula for the area of a right triangle, which is 1/2 * base * height. In this case, the base is AB = 9 cm and the height is AD = 12 cm. So, the area of triangle ABD is 1/2 * 9 cm * 12 cm = 54 cm².

Triangle BCD is also a right triangle because the sum of the squares of the two shorter sides (BC and CD) equals the square of the longest side (BD). So, the area of triangle BCD is 1/2 * BC * CD = 1/2 * 14 cm * 13 cm = 91 cm².

The area of the base of the prism (quadrilateral ABCD) is the sum of the areas of triangle ABD and triangle BCD, which is 54 cm² + 91 cm² = 145 cm².

Step 2: Find the height of the prism. The volume of a prism is given by the formula base area * height. We know the volume of the prism is 2070 cm³ and the base area is 145 cm². So, we can find the height by dividing the volume by the base area: 2070 cm³ / 145 cm² = 14.28 cm.

Step 3: Find the area of the lateral surface. The lateral surface area of a prism is the perimeter of the base times the height. The perimeter of the base (quadrilateral ABCD) is AB + BC + CD + DA = 9 cm + 14 cm + 13 cm + 12 cm = 48 cm. So, the lateral surface area is 48 cm * 14.28 cm = 685.44 cm².

So, none of the given choices are correct. The area of the lateral surface is approximately 685.44 cm².